Here, White's move creates an opposition of stones, forming a shape called keima. The position can be called opposing keima or knight's check. If it occurs in the corner, like here, it is called a small knight approach (of the corner). In these situations, where the checked stone is on the fourth line, the main purpose of is to undermine the stability of the stone (see basic strategy), whereas the one-space check blocks the development. In particular, aims at part of Black's base at a. Black's replies vary, because there is no urgency in this situation. The choice will depend on the surrounding position and overall strategy.
Jeff: I agree -- this isn't urgent. But the goal of your site seems to be building a model of Go from the foundations up. In "The balance of stability versus development" (above), you define urgent moves as those which provide stability for large groups. In "The Contact Play", you point out that the stability of the one stone's stability is in danger and that the situation is urgent. This leaves a gap: what makes the Contact urgent and the Keima not? (If explaining this will take away from the goal of your article, I won't be offended; please delete this comment when you address it (either by choosing to ignore it or by adding the extra explanation).) Thanks!
''Answer to Jeff: stability has two main attributes, the amount of liberties and connectivity. With a contact play, the liberties of both stones in contact are immediately reduced, reducing the stability of both stones. This is not true for the keima approach. Hence the contact play creates an urgent situation, whereas the keima approach doesn't.