There is a variety of reasons, and there are a variety of ways, to customise a doll.
Some reasons to customise a doll may include wanting to create a doll that looks like you or your child, a doll that looks like your original character, or a doll that looks like a character in one of your favourite books, tv shows, or films, and one isn't available from the company that is adequate without alteration.
People also customise dolls which are bought cheaply on the secondary market that are in need of some sort of repair - commonly the original child who owned it has cut the hair, or in some other way taken very poor care of the hair, or in some cases, it was just a very well loved plaything whose hair was brushed so much there as been a great amount of loss to the wig. Removing the old wig and replacing it with one bought from a doll parts supply company can be a very cost effective way to repair the doll.
Other common customisations are ear piercing, and the addition of freckles, applied to the face of the doll with acrylic paint, coloured pencil, or some other means. One of the less common means of customisation, due to the skill involved, is eye swaps, where the eyes of two, or more, dolls are removed, and exchanged.
Here are some examples of the customisations that I've made to dolls: