A tyke is a child, especially a small one. A nursery school is full of tykes.
Little kids are a handful, as all parents and teachers know. Maybe that's why there are some slangy words for them, such as rugrat and tyke. Tyke is a very informal word: a letter from the principal wouldn't call a kid a tyke. However, an uncle or friend of the family might say, "How are you tykes doing?" This word is a little old-fashioned, but it's still used.