Noble knights and other such stuff
Along with Orcs, Humans are the other original race from the previous WarCraft games. The last time around, though the official storyline had them winning, it was the Orcs who did the spanking. It was difficult to argue with a lusted ogre. Still, Humans developed some traits in WC2 that seem to have carried over to the sequel. They were versatile, sneaky and (bloodlust aside), had a nicer spell repertoire.
As it stands right now, in WarCraft III they are arguably the most powerful race. Certainly, they are the most adaptable. The Human player has excellent tools at his disposal; be it for rushing, turtling and teching, support casters, cheese tactics or air power. They have the most versatile heroes and certainly the most powerful combination of heroes. Far from overpowered, they take a fair bit of skill to play and in fact the other races should aspire to have such a variety of strategies.
Humans just aren't the best at any single thing. Knights are fodder for Druids of the Claw and Tauren, though fortunately they are quicker. Inner Fire isn't on the same plane as Bloodlust, and Polymorph isn't as deadly as Possession. Gryphons excel at combat with ground units, being the most capable of holding their own with anti-air like Archers and support casters, but their ability to assault a base isn't on the same level as Chimaeras and Frost Wyrms. Healing comes earlier than it would for Orcs but conversely isn't as powerful. The Paladin is one of the weaker heroes in the game. If it wasn't for his partner heroes, he'd be useless, actually.
That's not a whole lot in the way of weaknesses. The Paladin aside, these are more like drawbacks to balance out the Human strengths. Even the Paladin is just a way of keeping the Humans reasonable.
First and foremost, Humans can do anything. A Human can do a hero rush faster than anyone else, since multiple peons can build the same building. Humans can use towers to rush or go creeping with. Their tier 1 units are very strong, even if not everyone respects the Rifleman. Footman/AM rushes are very effective, as you will see in the demos. A Human can have the fastest opening of any race. Any kind of rush - hero or tier 1 units - can come sooner from a Human than it would from Orc, Undead or Night Elf players.
Tier 2 opens the floodgates with Mortar Teams and support casters who are immediately useful. Out of all the siege units, the Mortar Team is the most effective at attacking enemy armies thanks to the big radius of their splash damage. The Priest's Heal and Sorceress' Slow are very powerful starting spells. When researched, Dispel Magic and Invisibility can put the hurt on a lot of foes.
Tier 3 gives the Human player Knights, Polymorph, Inner Fire, Steam Tanks and Gryphons. It should also give his opponent complimentary vaseline, if he hasn't got it already. Humans simply aren't weak at any stage of the game.
Finally, the Human heroes are disgustingly powerful. We'll get into the specifics later, but the combination of all three blends together like it does for no other race.