Simile is imaginative comparison of a partial affinity of 2 objects. It is used with the help of link words: like and as (also: to resemble, to seem, to look like).
As well as a metaphor, it has the tenor and the vehicle.
E.g. The rainbow - is the tenor and its descriptions are vehicles (words after as)
Both similes and metaphors compare things, but they do it in a different way.
We can see their formulas: 
As we see on the picture metaphor makes more direct comparison of two objects.
In everyday life we use them and we don't give attention to it, but without metaphors and similes our favourite songs and may be our life would become boring. You can check it here http://www.youtube.com/watch?v=zNFeAgUzpEQ