His mom tells him this because it's something like an other parent tells you. For example, you might where different clothes on different events like your birthday, vacation, holidays, etc..
By saying this shows Ash that he's ready for a new adventure - since he's exploring a completely new region, making new friends, catching new Pokemon ; a whole new lifestyle.
His mom probably doesn't say it word for word in every anime series, but she relates to it to show Ash how he's ready to take on a new adventure and become a new hero. He wears a different outfit in every series - even though it looks similar.
Hope I helped! :)