Here is a link to an explanation I found helpful: http://www.studyspanish.com/lessons/persa.htm

Gustar, as a verb, describes an object pleasing someone. When you say "me gusta x" you're saying that x pleases you. "Me" is an indirect object indicator. When you say "le gusta x," you're are saying that x pleases le, which refers to he/she/it and requires clarification. Given your example, "A mi hijo le gusta la cuna," you're saying "the crib pleases he/she/it, which is my son."

I understand the le or me I don't understand the "A mi" part. I guess it means "to my son or for my son"

Thank you Gumbee-very helpful