Why the blues scale?

The blues scale provides 2 types of soloing resources. It can provide a scale for a minor chord as well as for a dominant chord. 

Therefore, in C major since the dominant chord (as with any major key) is the 5th or G7, you would use a blues pattern here. 

Also, keeping on the example of C major, you may use the relative minor or A minor  blues over anything on that key.  

A bit more on superimposing the blues scale in a later post.