First, you must understand that air is a fluid, as is water.
Now imagine a boat under way and experiencing a cross current. To achieve a desired track, the person steering the boat has to allow for the cross current, by pointing the boat into the current by an amount determined by the speed of the cross current and the speed of the boat. The difference between the resultant heading of the boat, and its track, is called drift.
An aircraft is handled just the same.
To fly down the runway centreline when there is a crosswind blowing, the pilot must allow for drift. The amount of drift is determined by the aircraft's approach speed and the strength of the crosswind. On arriving at that point on the runway at which he has to flare to reduce the rate of descent, the pilot will now use the rudder to "push" off, that is, reduce the drift just before touchdown. This reduces the loads on the undercarriage.
In limiting conditions, where you might have a very wet runway and a strong crosswind, it is quite acceptable to land with the drift still on.