With the ascension of his father to the throne, Prince William will go from being simply the Duke of Cambridge and an heir to the throne to being Prince of Wales (and Duke of Cornwall and Duke of Rothesay) and the heir apparent to the throne. However, it's not quite an automatic thing.
Technically speaking, the heir to the throne must be assigned those titles. Prince Charles, for instance, has been his mother's heir since birth and has been first in line for the throne since 1952, but the Queen did not formally grant him the title Prince of Wales for several years. This was, reportedly, because Charles was still a child and she wanted to ensure he understood his duties before investing him with the title; since William is a long-serving adult working royal, that wouldn't be an issue when it comes to his turn.