pinch back (syn. pinch out)
To remove the growing tips on main stems, usually using the fingernails of thumb and forefinger, in order to induce branching and thereby thicken and strengthen the plant.

Here is a link that might be useful: GardenWeb Glossary of Botanical Terms

Some plants tend to be tall and leggy, that is, without many branches, if they are allowed to develop without hand pruning, called "pinching back." I'll pick coleus as an example. When the plant begins to develop, if you pinch off the tips of the branches just above a leaf joint, TWO branches will develop there in place of the one. By pinching off the tips of new branches in this way, you train the plant to branch more, and also keep it from getting excessively tall and scraggly. You end up with a fuller plant.
In addition,certain coleus, like some other foliage plants, tend to "go to seed" somewhat early. If allowed to produce seed, the plants have fulfilled their life mission- reproducing their species- and they want to then die. If you are careful to keep any developing flowers pinched off, the plant will continue to grow because it wants to make seed before it dies.
Many flowering plants can benefit from "pinching back" in the same way. You get more branching and a more full, attractive plant. Also, if you will pinch off flowers when they begin to fade, the plant will be stimulated to produce more flowers because that means more seed. A plant (or an animal) lives primarily to further the species. If it didn't, the species wouldn't exist.

I didn't understand it either, but it's as easy as it sounds. I had to go look up the how-to of pinching back a mum and was thankful that it really was as easy as I (didn't) make it out to be.

(Incidently, for mums, you want to pinch it back to about 6-8 leaves from Spring through July 4th or so, then leave it be. That promotes fuller mums.)

Hey, it worked! My mums are looking mighty fine right now...can't wait til they start blooming!

What else will benefit from a good pinching?

Pinching...like all pruning....is a growth STIMULATING practice. Many people don't understand that, so don't feel like you are alone. The act of removal of the terminal growing point encourages new growth from buds that would otherwise remain dormant for the life of the plant. It is entirely hormone directed.

A good pruner (and pincher) will learn to make cuts above those buds that are growing in the direction they would like the plant to grow. In the case of succulent stems, a pinch is likely to stimulate new growth in the preceding nodes.

Just remember to cut or pinch at a node to get the most benefit from the procedure. Leaving a stub might not give you the results you are looking for.