When you define a similarity, you define it necessarily relatively to one or more parameters.
To elaborate more on Anony-Mousse, well behaving similarity can be roughly defined as the 1-distance (distance of 0 means a similarity of one).
In very simple cases, you can easily distinguish the parameters you want to compare.
But it's not always easy, especially when their are numerous parameters and/or unknown underlying parameters. For instance imagine you can compare the similarity of 2 movies based on the actors that played in them, and you can define a similarity based on the city where the story is mainly based, etc.
You can easily imagine that those similarities don't need and won't generally be identical.
Now, let's say you want to define a general measure similarity of 2 movies. How can you do it ? There isn't a unique answer. And that's the kind of questions movie recommenders have to struggle with. Some even make contests to find the best answer (http://www.netflixprize.com/).
To understand better, you actually want to find a way to compare movies, so that when you know somebody liked one movie, he will most certainly like all similar movies, based on the note he gave of the movies he previously watched.
Actually all this comes to identify the set of parameters that truly influence the appreciation of a movie. In this case, the winners of the prize used an SVD approach to identify and isolate underlying correlated dimensions (that are not necessarily conceptually understandable and are more complexe to figure than "actors" or "places").