According to Paramount, canon is anything live-action that appeared on screen in a movie or a regular broadcast. So TAS would not be canon under this definition, but all the series and the movies are, including the latest one.
As for the purpose of canon...well, I have to back up. What's important to me
about canon isn't minutia about how this thing occured on star date ____, so how could event X have happened only a month later? Or about uniform colors...or even details of the early life of various characters. I can overlook all those little inconsistences, and I can even overlook some fairly important inconsistencies.
What's important to me
is that any movie or series marketed under the name Star Trek needs to fit into the recognizable Trek universe. So that, for me, is the reason for worrying about canon.
Yes, I'd like everything new to fit in with what's come before, but I know that realistically that's just not possible. You can't make 40-some years of TV shows and movies, all written and produced by different people, all made under vastly different circumstances and during vastly different times and all trying to appeal to newer audiences, fit together. So long as they kind of fit together, that's the best I can hope for. And I'm OK with that.
So that is to me what canon is for: To keep it recognizably Trekkish.