For my first research project in microbiology I've chosen to determine the effectiveness of sanitizers and soaps in killing bacteria from our hands, however, after putting the bacteria on agar plates using cotton swabs, why do we incubate them? Won't their numbers increase and give us the wrong results?
This is a very standard method. The idea is that you have a culture of bacteria on an agar plate. During the incubation each bacteria forms a colony. After a few hours of growing the colonies grow and become visible for human eyes. So you can easily count them.
Then you can compare the number of colonies before and after washing your hands with the sanitizers and soaps and find which method has the lower amount of colonies on average and therefore whihc one is the most efficient one.
When you swab the agar plate with your sample, what you're doing is spreading out all the bacteria in your sample so that each cell is able to grow separately from the other cells and form an isolated colony.
Since bacteria are microscopic and you can't actually see them directly in your sample, you need to allow them to grow a little until they form a colony and you can actually see them with your eyes. The assumption we make when we use this method to "count" bacteria is that a single cell gives rise to a single colony on the plate. That's why we call the cells "Colony Forming Units".
This might be of some help: https://en.wikipedia.org/wiki/Colony-forming_unit