See the picture right above your post!!
Sucker is a new stem that grows out of the V-shaped crotch between a stem and a branch. Not everyone prunes them. If left to grow it will become a new stem. Sometimes those new stems are not very productive, but sometimes the new stem will also flower and fruit. But it is competing for nutrients with the original plant. If you leave all the suckers, you may get more tomatoes, but smaller.
Un-pruned, your tomato plant will get VERY bushy:
Since I grow in humid climates, I keep my tomato plants more pruned (pinch out the suckers and also clip most of the branches that are growing in towards the center) to open them up and make more air circulation through the plant. IME, it helps cut down on disease problems.