Horace Slughorn was once a student at Hogwarts School of Witchcraft and Wizardry and was sorted into the house of Slytherin. It turned out that he had a knack for potions and developed very high skills in these areas. Later on in life, around the same time as Albus Dumbledore, Horace joined the faculty of Hogwarts and took up the position of Potions Master and head of Slytherin. While he was teaching he started a group now known as the Slug Club which was for his brightest and most talented students. Most of these students ended up famous or well known, which provided Professor Slughorn with several positive benefits later in life, including free Quidditch tickets and connections to The Daily Prophet. Although, unlike most Slytherins, he was nice to all students regardless of things like 'blood status', he tended to have favorites and often ignored the ones who seemed not to be very talented. In the school year of 1942, Horace hosted a supper in his office consisting of only Slytherin boys, most notably Tom Riddle, who eventually restyled himself as Lord Voldemort and became the most powerful dark wizard of all time. At the conclusion of the meeting, Tom asked Professor Slughorn about the dark magic of Horcruxes, claiming to have stumbled across the subject innocently during research in the library, and Professor Slughorn reluctantly explained the process of creation and how useful they are. Later on in life, Tom would have a total of seven different Horcruxes, which shamed Professor Slughorn as he was the one to have given Tom the information regarding them. He later modified his own memory to stop this information ever getting out. For the next few years, he continued to teach at Hogwarts, where his students included Lily Potter, one of his favorite, owing to her natural aptitude for potions, and Severus Snape, his eventual successor. In 1981, Professor Slughorn resigned from Hogwarts and began a life on the run, fearing the death eaters would try to recruit him.
Half Blood Prince
During the summer holidays Headmaster Albus Dumbledore brings a confused Harry Potter with him to help recruit Slughorn as a teacher at Hogwarts, despite his being retired and in hiding, and having previously refused to return to Hogwarts. When they arrive in the Muggle village of Budleigh Babberton, they find the door to the house he is occupying hanging off of its hinges, and inside the broken furniture and blood splattered over over one of the walls seem to testify to a vicious attack. However Dumbledore is not wholly convinced by the show and soon finds his old colleague magically disguised as an armchair, having wrecked the house himself to put off any recruiting Death Eaters.The blood, as it turns out, is dragon's blood, something with which Dumbledore is very familiar, having conducted considerable research into the twelve uses of dragon's blood. Knowing that Slughorn will be unable to resist the prospect of 'collecting' Harry (as he has so many other renowned witches annd wizards), Dumbledore appears to give up on recruiting Slughorn and leaves with Harry. As he thought, however, Slughorn's own nature is too powerful for him to resist, and Slughorn agrees almost immediately to return to Hogwarts after all. During his teachings, he had Harry Potter as his favorite student because of Harry's said to be extraordinary potion-making that he got from his mother, Lily Potter, one of Slughorn's favorites( although it was the help of the half-bood prince that aided Harry), and awarded him with liquid luck also known as Felix Felicis that Harry later on used to get Slughorn's precious memory of the night that Tom Riddle asked him about Horcruxes. 
During the Battle of Hogwarts it initially appears that Professor Slughorn has run away scared, but it later emerges that he went to collect reinforcements from Hogsmeade to join in the Battle. Towards the end of the battle, Professor Slughorn duels capably alongside Kingsley Shacklebolt and Minerva McGonagall whilst fighting Lord Voldemort. Horace became Slytherin's Head of House when Snape was made Headmaster of Hogwarts.
Portrayals within films
Horace Slughorn is portrayed in Harry Potter and the Half-Blood Prince and Harry Potter and the Deathly Hallows Part Two by Jim Broadbent In the films he is neither extremely fat nor sports a moustache.
An enormously fat, bald old man... The wand light sparkled on his shiny pate, his prominent eyes, his enormous, silver walrus-like moustache...
Slughorn is also short (his head barely reaching Dumbledore's chin), with legs so short that they don't even reach the floor when he sits on a sofa. He has pale, gooseberry coloured eyes.
With his highly polished buttons, velvet jacket, lilac silk pyjamas, and personal piano which he takes with him from Muggle house to Muggle house, it is clear that, even in hiding, Horace Slughorn is a wizard who won't do without his comforts. His comforts, however, can also be his weaknesses. One such comfort, the warm reflected glow he feels at having 'collected' witches and wizards who go on to fame or renown, is a particular weakness. Whilst acknowledging it is wrong to have favourites, Slughorn has never been able to resist this tendency. Of course, it also brings him numerous more tangible comforts later in life as these people remember him and send him various gifts. On occasion, however, such as in Tom Riddle's case, this greed to collect talented students, blinded him to overlook the young Voldemort's true nature and intentions, despite the fact that Riddle was asking him about Horcrux creation, considered some of the darkest magic.
Slughorn is generally magnanimous and seems unperturbed by being 'caught out', for example by Dumbledore seeing through his armchair disguise and by his failure to set a Dark Mark above the house as the final touch suggesting that Death Eaters had come calling for him. He is also quick to change his mind (and is often entirely unabashed by this), for instance in his opinion of Dolores Umbridge, which turns from sympathy to dislike in mere seconds.
Unlike many Slytherins, Slughorn is not overly interested in 'blood status', though he does seem to hold an underlying belief that 'Muggle-borns' generally ought not to be as talented as 'pure-bloods'. This might simply be down to the Slytherin culture in which he spent so much time - it has certainly not prevented him from having 'Muggle-born' favourites and adding them to his 'collection'.
His tendency to shy away from unpleasantness, discomfort, and danger makes it easy to believe he has deserted the fight during the Battle of Hogwarts. Whether because Harry has already urged him once to "be brave" (when persuading him to give up his true memory of the Horcrux conversation with Riddle) or because he considers it the best way to make amends for telling Riddle what he told him (or for some other reason), Slughorn does return to the Battle and fights bravely.
Magical accomplishments and skills
Horace Slughorn is a highly talented potions expert, whose skills seem to have brought him some renown (hence Albus Dumbledore's conviction that Voldemort's Death Eaters would seek Slughorn out and put his "considerable talents" to terrible use in service of Lord Voldemort). In Harry's fifth year at Hogwarts, Slughorn accepts the position as Potions Master at the school, a position previously held by Severus Snape. It is the second time he has held this post at Hogwarts, having taught the subject for many years in the past. The books portray him as well-liked and extremely knowledgeable in this and other areas of magic (including dark magic).
Slughorn is accomplished in other areas also. His apparent ability to stay hidden from the Death Eaters for so long implies he is very good at the various charms he employs to make his temporary home look as though it has already been ransacked and devastated. During the Battle of Hogwarts, Slughorn also shows himself to be very capable at duelling.
Dumbledore also describes Slughorn as having "an uncanny knack for choosing those who would go on to become outstanding in their various fields." Whether, for Slughorn, this is a magical sense or just a reflection of his own ambitious nature is unclear.
Horace Slughorn does not have many prominent physical possessions, as he has spent the last year on the run from Death Eaters, believing that they might try to recruit him. Despite this, he has managed to live comfortably in various Muggle houses, even transporting his piano with him to wherever he was temporarily staying (though there is no reference to any piano coming to Hogwarts with him).
However Slughorn does have one very prominent and valuable possession - his real memory of Tom Riddle asking him about Horcruxes. This memory is immensely important to Albus Dumbledore, who sees it as the key to understanding how Voldemort can ultimately be defeated.
Besides this, he has a wand of unknown core and material, a fascinating hourglass that measures the intensity of a conversation, and his bag of potions. For a short time, he also has in his possession a bottle of poisoned oak-matured mead, given to him to give to Dumbledore. Slughorn, not realising the mead is poison, administers it as a 'pick-me-up' to Ron Weasley to aid his recovery from a particularly strong love potion.