What Heimer does best is ratchet up the pressure, building up a creep wave, slowly forcing it closer and closer to the enemy tower by moving his turrets forward, before dumping a mass of creeps on the enemy point to neutralise it. He isn't great at killing enemy champions, but he controls the lane like a boss.
This works best against people who cannot push. Champions like Maokai or Cassiopeia can destroy an infinitely large creep wave with a couple of spells. A single-target champion will have a hard time dealing with this creep pressure.
It also works best against enemies who can't kill your turrets. Any ranged AD champion with more than 500 range can kill your turrets without taking more than a couple of turret counterattacks, if they're behaving intelligently. (If you just run up to a turret, with no creep wave to steal attention and protect yourself, you will take a bunch of damage from it.) Most mages can take them out fairly easily too.
The best counters to Heimer are any champions who can push as well as he can. Because Heimer can only push, he's not a nuker, he doesn't really have any other strengths, if you nullify that strength, his lane becomes a liability.