The human is the base character, all other races are compared to him. Humans can choose any class, and are average at everything. Humans tend to go up levels faster than any other race, because of their shorter life spans. No racial adjustments occur to characters choosing human.
Half-elves tend to be smarter and faster than a human, but not as strong. Half-elves are slightly better at searching, disarming, perception, stealth, and magic, but they are not as good at hand weapons. Half-elves may choose any class.
Elves are better magicians then humans, but not as good at fighting. They tend to be smarter and faster than either humans or half-elves, and also have better wisdom. Elves are better at searching, disarming, perception, stealth, and magic, but they are not as good at hand weapons. Elves may choose any class except Paladin.
Halflings, or Hobbits, are very good at bows, throwing, and have good saving throws. They also are very good at searching, disarming, perception, and stealth; so they make excellent thieves (but prefer to be called burglars...). They will be much weaker than humans, and no good at bashing. Halflings have fair infravision, so they can detect warm creatures at a distance. Halflings can choose between being a warrior, mage, or rogue.
Gnomes are smaller than dwarfs, but larger than halflings. They, like the halflings, live in the earth in burrow-like homes. Gnomes are practical jokers, so if they can kill something in a humorous way, so much the better. Gnomes make excellent mages, and have very good saving throws. They are good at searching, disarming, perception, and stealth. They have lower strength than humans so they are not very good at fighting with hand weapons. Gnomes have fair infravision, so they can detect warm creatures at a distance. A gnome may choose between being a warrior, mage, priest, or rogue.
Dwarves are the headstrong miners and fighters of legend. Since dungeons are the natural home of a dwarf, they are excellent choices for a warrior or priest. Dwarves tend to be stronger and have higher constitutions, but are slower and less intelligent than humans. Because they are so head-strong and are somewhat wise, they resist spells which are cast on them. Dwarves also have good infravision because they live underground. They do have one big drawback though. Dwarves are loudmouthed and proud, singing in loud voices, arguing with themselves for no good reason, screaming out challenges at imagined foes. In other words, dwarves have a miserable stealth.
Half-Orcs make excellent warriors, and decent priests, but are terrible at magic. They are as bad as dwarves at stealth, and horrible at searching, disarming, and perception. Half-Orcs are, let's face it, ugly. They tend to pay more for goods in town. Half-Orcs do make good priests and rogues, for the simple reason that Half-Orcs tend to have great constitutions and lots of hit points.
Half-Trolls are incredibly strong, and have the highest hit points of any character race. They are also very stupid and slow. They will make great warriors and iffy priests. They are bad at searching, disarming, perception, and stealth. They are so ugly that a Half-Orc grimaces in their presence. They also happen to be fun to run...