Stilly, look at the main stem or main two stems of your tomato plants. Follow the line of that (or those) two stems. There will be short branches off of the main stems. In the axil between the main stem and the short branch will be another branch. This is what is called a sucker.

Many people choose to pinch off those suckers to allow the main branches to bear larger tomatoes. The suckers will also bear, but what can happen is that the plant will develop so much fruit that the fruits will be as large as they otherwise would be. If you do not sucker tomatoes you get more fruit, but smaller fruit. More recent research has indicated that you will probably get the same over-all yield in poundage whether you pinch off the suckers or not.

One advantage of pinching off suckers is better airflow and possibly less desease as the result.    If you are wanting big slicing tomatoes or to impress the neighbors with the size of your tomatoes, sucker them. Or if diseases related to poor airflow are a major problem, sucker your tomatoes. (they are also easier to stake and keep off the ground, or to keep from tobbling over cages or stakes if you sucker them. You will get more tomatoes but smaller tomatoes if you do not sucker, and the vines will probably succomb more quickly to disease or fungus if you do not sucker. But where I live, the heat and humidity of full summer are going to result in disease no matter what. I'm better off starting a second planting about 4-6 weeks after the first if I want tomatoes up to first frost in October.

I may sucker tomatoes early in the season, for no good reason, but have not routinely suckered them for a number of years. If I lived in a cooler climate with a shorter growing season and fewer disease problems that could be effectively controlled by attending to air circulation, I might be more inclined to go out weekly and pinch out the suckers.

Where there is a long growing season and high humidity, such as you and I have, and where disease is likely to limit tomato production late in the season (that is an issue here, and I'm guessing where you are in Texas,) you can also root some of the early suckers, using rooting hormone and vermiculite and/or perlite, and plant them early to mid summer to bear in late summer through fall, and take out the early tomatoes when disease begins to seriously reduce production, or to limit the spread of disease.   Rooting the suckers is faster and less labor intensive than starting seeds to plant mid-season.