Tivo Explained?

With a busy schedule involving school and work, I am not able to catch many of my favorite shows. DVRs seem a little spendy compared to a Tivo. The thing is if Tivo is cheaper, why? Do you HAVE to do a monthly thing or something? Does it only work with a monthly contract?

Could someone simply explain what Tivo is and how it works AND if it is worth the $$