Immensely is an adverb that means vastly, or very, or hugely. An immensely good time is a really, really good time.
If you know that immense means huge, then you probably already have a sense of what immensely means. It's a word for describing the enormous degree of something. A New York Times bestseller is an immensely popular book. Any offensive lineman is an immensely large human being. The earth is immensely old. A mouse can't be described as doing anything immensely, but an elephant does things immensely all the time.