It depends on who you ask. The Oxford Dictionary entry for unique defines it as:
being the only one of its kind; unlike anything else:
Some people, such as the writer of this blog or this list of English errors, think that unique should only ever refer to one thing:
Unique means (sometimes I can’t find any other way than to just repeat myself) one of a kind—there aren’t any more like it anywhere else—if this one disappears, then it will be extinct—you can search and search all over the world, but you won’t find a second one—after they made this single one, they broke the mold and threw the pieces into 27 different trash cans so that no one would be able to make another one.
People who follow this view will say that terms like "very unique" or "extremely unique" are not proper English. This is why you may have been told that they do not make sense. However, this is a very prescriptive view which says that English ought to be a certain way. Not everyone thinks that "very unique" is unintelligible, and other dictionary entries just say unique means:
very special, unusual, or good
In short, there is no one opinion on how unique should be used. Some people use it as you have, and others think you would be wrong. It all depends on what you think the definition of unique should be, and even dictionaries disagree on this.