A cutting point is an empty point between two chains of stones. If the opponent plays at that point, the two chains are cut.
If the cutting stone can be captured immediately, there is no cutting point.
In this position, a white move at the marked point puts itself in atari. Black's stones are in fact connected by a hanging connection.
White can of course threaten to cut. After White 1, there is again a cutting point at a, so Black now has to connect there. White 1 is called peep.
It is important to defend your cutting points.
There is a general question about how to defend. It is one of the simpler issues about good shape.
In this diagram, the marked black stone protects the cutting point in a fancy way (see keima protecting the cutting point). If White cuts, her cutting stone will be captured in a ladder towards the bottom, or in a loose ladder towards the left. So in a broader sense, there is no cutting point, yet this position still contains some aji.