Pruning tomato plants is a technique used by some gardeners and completely unknown to others. It involves pinching off the "suckers" that grow between the main stem and branches of a tomato plant. It allows more water and sunlight to reach the plant, allows air to circulate freely around the plants and theoretically results in earlier fruit and healthier plants.
I learned about pruning tomato plants from my grandparents. In past years, I started off with good intentions and trimmed off the suckers when the plants were young, but then I would get busy and not keep up with it throughout the season. This year, I didn't prune them at all, and you can see what a tomato jungle it is!
I'm considering this year an experiment. I expect the unpruned plants to produce more tomatoes than the pruned plants. We'll have to wait and see about the health and timing of the first tomato. If you have any thoughts or experience with pruning tomato plants, please share!