To start, I'm going to say this is in general. You might have success putting a top lane hero mid lane if that top lane hero counters the hero in mid lane. But overall, this is why:
Bottom lane is closer to dragon, and is harder to gank than mid lane. Two well placed wards will keep you safe. Because of this, you put the AD Carry and support bottom lane. This gives you a safe lane for the AD carry to farm in, and gives you more control over dragon.
The AD carry is a ranged hero such as Kog'maw or Graves. They tend to scale more off items than levels, though obviously they get stronger as their skills level up. The support is a hero that generally has CC, a heal or shield, or some sort of steroid for the carry (or some mixture of those). Their job is to keep the carry alive and give him an easy lane to farm in.
Mid lane is a solo lane, and thus profits from having more experience than bottom lane. Mid lane is also in between bottom and top (duh!), and thus can gank both lanes fairly easily. You also get good farm in this lane. Thus, you put an AP hero who scales off levels strongly and needs farm to scale into late game.
Top lane is also a solo lane, but is generally more farm oriented because of how far away from the early game action it is (dragon + bottom/mid). You also need some sort of tank late game, and generally they need to farm. So you put a tanky damage dealer (a bruiser) top lane. They get solo exp and farm, and deal a good amount of damage (though not as much as the ADC) while being quite tanky.
And then you have the jungle. The jungle has possibly the most complex role in the game. In short, you're there to gank lanes, clear the jungle, and do whatever else the team needs you to. If your team is missing a hard engagement hero, you might pick Amumu, for example. Junglers range from very tanky to rather squishy, and it's all about what your team needs. But mostly, you jungle because it gives you the extra gold and exp from the jungle, gives top lane a solo lane, and allows you to gank and kill all three lanes from "the shadows", as it were.