What is 'the House' in American politics?

The American political system has three centres of power. These are  the President and the two chambers in the American Congress the - Senate and the House of Representatives. 

'The House' - also sometimes known simply as Congress - is the bigger body because congressmen are elected at a local level while the Senate consists of two senators lected from each of the fifty US states. Though the states vary substantially in population size, each has equal representation. The intention of the founders was to ensure that the larger states did not dominate.

All laws must originate in Congress. They the must pass up through the Senate and then be approved by the President. This is to ensure that legislation comes directly from local representatives, though the increasing use of presidential 'executive orders'  has been controversial in this regard.

The legality of any legislation is ultimately decided by the Supreme Court. Judges are appointed for life by presidents. Their role is to interpret law in the context of the US Constitution.

Democrats & Republicans

At present the Presidency & the Senate are controlled by the Democrats. The Republicans have a small majority in the House. Legislation has to pass from he House to the Senate and finally to the President. 

Because the two main parties (the Republicans & the Democrats) have major philosophical differences most legislation is contested.