The Commerce Compromise is essentially the sharing of control over taxation and regulation of commerce between the states and the central government. 

It was necessary because under the old Articles of Confederation states taxed and regulated all of the commerce, and so crippled trade by taxing each other's imports, and the central government could not bring order to state declaring "trade wars" on one another, nor could the central government raise its own sources of revenues. It was entirely dependent on the state to fund it. 

It's important because it gave the federal government new powers and allowed it to increase control, as commerce among the states, and overseas became more and more important to the states. In the long run, it meant greater federal supremacy over the states.