Cooties is a made up disease, children use to avoid one another.
Cooties is "contagious", so when one child doesn't want to play with another child, they spread a story in school, for example, saying he/she has cooties, and that's why they don't want to play because they don't want to catch it.
Because cooties is "contagious", someone who plays with a child labelled with cooties is also said to be "infected", and therefore avoided.