Antibiotic resistances are a main tool of bacteriology. It has many applications, mostly for selection purposes.
If you bring a plasmid (a DNA fragment that works like a little genome) into bacteria, you usually have a antibiotic cassette on it. The bacteria that take up the plasmid will express proteins that make them resistant to the antibiotics and will thus survive and/or grow, while bacteria without them will die or not grow. After bacteria have taken up the plasmid and are selected for it, you have to keep growing them in the antibiotics, as they would lose the plasmid after a while without it (replicating the plasmid costs time and energy, if they don't need it it will get lost as the bacteria without it will just grow faster).
Another application is the selection for successful transductants after bringing a gene into the bacteria with viruses.
It can also be used as a negative selection tool, to select for the bacteria that have lost the sensibility to antibiotics (you have to screen for them on plates with the antibiotics and without them).
This is only a selection of the most broadly used applications of antibiotics. It's an elementary tool of our work.
Now about the color changing part. There are multiple different screening methods that rely on colonies that change color. Bacteria do however not just change color when they express a resistance gene. We use multiple antibiotics (I work with ampicillin and tetracycline on a daily basis) and they don't change color only because of the resistance cassette.
I don't know to what screen or gene you were referring to