The description of the imp varies slightly depending what mythology you're taking it from, what book you're reading or what game you're playing. Sometimes it's a tiny devil or evil spirit, an offshoot of Satan - this stems from the original meaning of the word, as an offshoot of a plant. Other fiction portrays them as crafty, pointy-eared goblins, while Indian mythology describes the imp instead as a genie-like creature that can grant its owner wishes. The imp in a number of recent games including MMORPG RuneScape is the stereotypical tiny devil - a miniature red devil guy with a pointy tail, horns and a trident. In any story or game where they feature, imps are notably weak, and will likely die with one good swing of a sword.
In fantasy roleplaying game Dungeons and Dragons, the imp is the smallest and one of the weakest of the creatures that fall into the category of devils. Unlike its more powerful brethren, the Baatezu, these tiny winged creatures rely primarily on subterfuge and trickery to advance in power and further their evil ends. They are only slightly more powerful than Hell's mindless hordes of lemures, but make up for their weakness with the abilities to take the form of a different creature or turn invisible at will. Imps often act as spies for more powerful devils and evil wizards.
Imp: CR 2; Tiny Outsider (Evil, Lawful); HD 3d8; hp 13; Init +1 (Dex); Spd 20ft., flt 50ft. (perfect); AC 18; Atk +7 melee (1d4 and poison, sting; Face/Reach 2 1/2 ft. by 2 1/2 ft./0 ft.; SA Spell-like abilities, poison; SQ DR 5/silver, SR 5, poison immunity, see in darkness, polymorph, regeneration 2; AL LE; SV Fort +3, Ref +6, Will +4; Str 10, Dex 17, Con 10, Int 10, Wis 12, Cha 10.
Skills and Feats: Hide +15, Listen +5, Move Silently +5, Search +5, Spellcraft +5, Spot +5, Sense Motive +10, Spot +12; Dodge, Weapon Finesse (sting).
Spell-Like Abilities: At will: detect good, detect magic, and invisibility (self only); 1/day-suggestion. These abilities are as the spells cast by a 6th-level sorcerer (save DC 10 + spell level). Once per week an imp can use commune to ask six questions. The ability otherwise works as the spell cast by a 12th-level cleric.
Poison (Ex): Sting, Fortitude save (DC 13); initial damage 1d4 temporary Dexterity, secondary damage 2d4 temporary Dexterity.
Polymorph (Su): An imp can assume other forms at will as a standard action. This ability functions as polymorph self cast by a 12th-level sorcerer, except that an individual imp can assume only one or two forms no larger than Medium-size. Common forms include monstrous spider, raven, rat, and boar.
Regeneration (Ex): Imps take normal damage from acid, and from holy and blessed weapons (if silver or enchanted).
It's occasionally been joked that Hell is actually ruled by an incredibly clever imp, who has managed to convince his subordinates into believing that they're actually being ruled by a more powerful super-devil they've somehow never seen.
Sources:
http://www.opengamingfoundation.org/srd/srdmonstersd.html
http://www.fantasysquare.com/ffmyth/imp.shtml