I just recently got a very bad haircut, and the worst part was the
fact that the hairstylist went to town with the thinning shears on my
head. My question is, what exactly do thinning shears do, so that I
can understand if my hair will thicken up faster than it will grow in
length. Also stated, do thinning shears cut certain hairs and leave
others long, or do they actually do something to the single hairs to
make them more thin? Thank you for your help.

Thinning shears only cut certain hairs and leave
others long, so by the time your haircut is done you have many
different lengths to hair. The thinning shears cut a few hairs at a
time in small groups not just one here or there. If not done correctly
you may end up with some areas thinner than others. Sorry you got a
bad cut.