"Family is very important to me."
This sentence can be broken down into two parts: the main sentence is かていはとてもたいせつです "family is very important." I'm guessing you get that part; you've managed to reach level 11 after all. The clause わたしにとって is a bit tricky; とって is the -te form of とる, "to take", so it literally means "taking to me" which is why it can be a bit confusing; however, にとって is a set expression meaning something along the lines of "as far as ... is concerned" or "to ..."
Knowing that, this sentence basically says "as far as I'm concerned/to me, かていはとてもたいせつです" thus "family is very important to me."