Role in Myths
Loki was born from the Jötunn Fárbauti (ON: "Cruel Striker") and Laufey/Nál (ON: "Needle"). Although he was accepted by the Gods of Asgard as the honorary member of their people, Loki proved himself a troublemaker for being a wily striker. Despite being naturally male, Loki's gender is actually malleable owing to his shapeshifting ability and with his mare form, he is the "mother" of eight-legged, Jötunn-horse hybrid Slepnir with the stallion Svadilfari.
In addition of Slepnir and his parents, Loki's other family members are Angrboða (ON: "Anguish-Boding") (with whom he sired three children Hela the Goddess of Death, Fenrir the Wolf Jötunn, and Jörmungandr the Midgard Serpent), Sigyn (with whom he sired Váli and Narfi and Váli (noted that the latter shares his name with Odin's son through marriage with Jötunn Rindr)).
In his early days among Gods of Asgard, Loki's pranks often brings troubles for his newfound allies. For example, in the tale of The Kidnapping of Idunn, he encited the wrath of the Jötunn Thiazi who then coerced him to bring Idunn for him only to nearly doomed his fellow Gods, since said goddess was the only one who can take care of her special apples which grant them their immortality. In the same tale, he also unwittingly angered Thiazi's daughter Skadi who demanded restitution for her father's death in the same incident (when Loki took Idunn back to Asgard with his falcon form, Thiazi caught them in the act and give chase with his eagle form all while recklessly entering the Gods' territory in Asgard in process, provoking the guards to kill him on the spot). Since Skadi proved herself more reasonable than her father and most of her kin despite her initial vengeful rage, the tension between her and the Gods was resolved without bloodshed.
Another examples of his pranks are annoying Thor through shaving his wife Sif's golden hair clean, interfering dwarf brothers Brokkr and Sindri's progress in crafting the Thunder God's signature hammer Mjölnir (which resulted the hammer's handle being shorter than intended) to win the bet he made with them, and giving a shady Jötunn the chance to get his hands on Freya, sun, and moon should he managed to complete the fortification around Asgard despite his apparent treacherous nature. In the latter's case, Loki was forced to swallow his pride to ensure said Jötunn's failure by distracting his horse Svadilfari and mating with it in process, culminating to the birth of Slepnir. Yet, it all nothing compared to the worst that Loki stored for them.
Powers and Abilities
Loki is depicted with many different powers at his disposal, in fiction and in folklore, shapeshifting seeming to be one of his specialties in the old tales while, as a god, it is specifically reasonable to assume he could pretty much do anything he desired - though he would not have anything like the power of a god such as Odin.
Unusual for a Norse god Loki was said to have a large degree of command over monstrous creatures such as trolls and giants, traditional enemies of the gods - though this could be down to the fact Loki himself is sometimes considered a half-giant and is the father of a few notable monsters himself. Also, while not on Thor's level, Loki seems to have a enormous degree of superhuman strength, causing earthquakes every time he writhes in pain.
In Modern Media
Loki is one of the most infamous of the Norse gods and has been described in many films, comics, videogames, and books, as well as traditional lore - his monstrous children are equally famous in the form of the giant wolf-monster Fenrir, the world-serpent Jormungandr and last his own daughter, the Norse goddess of the underworld named Hela (who is the child of the immortal giantess Angrboda, Loki's first wife).
Some of the most famous incarnations of Loki in modern fiction has been the supervillain in Marvel Comics, in which he is basically a slightly updated and toned-down version of the trickster god of folklore and the villainous Loki from the Son of Mask - who was considerably less like his mythical counterpart and more in line with a run-of-the-mill evil magician/prankster.
Loki has also appeared in the Stargate series - in which he was a rogue Asgardian conducting illegal experiments on humans - this version of Loki is even less like the mythological one than the version in Son of Mask and is in effect an archetypical alien invader akin to the Greys seen in series such as the X-Files. Other incarnations of Loki and characters inspired by him have appeared in innumerable works of fiction - probably too many to list here, these are just a sample of the few that are aware of by all.