Can anyone link me to an explanation of meditation or offer any tips on how to do so?

I don't want to offend anyone with my ignorance, but thus far in my life I have not truly understood meditation. I have been under the pretence that it is the act of clearing one's mind, but this definition needs quite a bit of work.

I have tried meditating under that simple premise quite a few times before but I find it extremely difficult to do so. I've been gifted with an expansive mind but with that has come difficulty in quieting it. Am I just not focusing enough? Or am I focusing too little? I also have difficulty in maintaining my attention span, but I assume fixing that is something that just requires discipline and practice.

Also as a little side question, what are some of the benefits to meditation that you've noticed? I appreciate all of the help in advance, and once again I apologize for my unfamiliarity of the subject.