The main point is so you don't have to hand over your password to let programs access your email. Why would a service need your email messages? Maybe to do cool analytics like etacts, or do an improved contact import that prioritizes the contacts by how often you correspond with them.
One thing that particularly annoys me is when websites like LinkedIn and Facebook ask for your webmail password so they can suggest new contacts based on your email history. They promise they won't store your password, but it is shockingly insecure.