An example you can practice any time is to set the cue ball in the exact center of the table, then line up a straight in shot into the side pocket (set the object ball maybe a foot or so from the cue ball).
If your next shot is on the right side of the table, you can cut the object ball slightly to the left instead of hitting it dead into the center of the pocket. This will send the cue ball towards the right half of the table to make that next shot easier. If your next shot was on the left half, you'd cut the object ball a little bit towards the right.
How to execute it - exactly the same way you'd execute a normal shot. You just aim to hit the ball a little differently.
It's a super valuable skill, and by learning to do it you also learn to build enough accuracy to not only make balls, but to make them hit one side of the pocket or the other. With that kind of accuracy you'll be a great shotmaker and will have an easier time on tables with smaller, tighter pockets. On those pockets it's harder to cheat the pocket, so it becomes more important to give yourself an angle where cheating would not be necessary... the cue ball will naturally travel in the direction you want.
edit: I guess I understand your question a little better now.
The closer a ball is to a rail, the less likely it is that it can hit the dead center of the pocket (because the rail itself obstructs the shot). Here's a classic situation that comes up all the time. A lot of players find this shot counter-intuitive. In the example below, it makes more sense to cut the ball into the corner than into the side. You might think "but it's a sharper cut into the corner, and the corner is usually a bit smaller than the side pocket, and it's also further away... why would I cut it into the corner?!"
Normally sharper and longer cuts are a bad thing. But in this case it's the easier shot. That's because you can't aim towards the center of the pocket in the side, it's blocked by the rail (which I darkened up to illustrate). Your margin for error is tiny, you barely can fit the ball into the 'shootable area' from this angle, and if the angle were much steeper it'd be literally impossible. But the center of the pocket IS accessible for the corner, and no rail blocks you, so the corner is a much wider target area. It makes for a target that's literally twice as wide.