"suckers" or something of the sort on plants? is that the little shoots that come out in the notch between the leaf and the stem?

Yes, but applicable only to indeterminate varieties. But removing them, commonly called pruning, has nothing to do with the health of the plant, just with the manner of the supports used, plant spacing, etc. The label "suckers" is an old misnomer based on the old-timer, long dis-proven belief that they "suck life from the plant". They don't and are the source of much of the plant's production.

Some prefer to prune plants, many don't. It is your choice. There is a FAQ here called "To Prune or Not to Prune" and if you search 'pruning' you'll find many discussions/debates on the pros and cons of it.

Dave

I am pruning this year to have plants that arent out of control. I also want to see if I get bigger matos out of it. I didnt do so well last year and the plants were a jungle! The more green leaves the more moisture the plants will need. So far so good, I have lots of fruits set and growing and my plants look neat and tidy.