"Daddy" is the name that many young children call their fathers. They start to use the name "Daddy" at about 2-3 years old and keep using it until about age 10-13. As children get older, they start to use the name "Dad" instead of "Daddy".
When parents speak to very young children, from 0-5 years, they often speak about themselves as "Daddy" or "Mommy" instead of using "I" and "me". For example:
Daddy doesn't like it when you throw your toys.
Of course, there's a lot of variation from family to family in what children call their parents and how parents refer to themselves.