If you have a dog, your dog depends on you. That means your dog leans on you and knows that you'll take good care of him. In this situation, your pet is dependent on you, and you're a dependable pet owner.
Your family probably depends on you to work hard at school, or to do your chores, or to help out with your little siblings. That means your family needs you, relies on you, and counts on you. They're dependent on you. And you're dependable.
Although we often talk about people depending on each other, we also talk about things depending on other things. To depend on something is to change, or to be different, based on that thing.
Will we eat lunch outside today? It depends on the weather. If it's sunny and warm, sure. If it's raining, nope. Our plans depend on the weather. However, this guy doesn't care! He's going to eat outside no matter what: his plans don't depend on the weather.
What color is the sand at the beach? It depends on where you are. Some beaches in Florida have white sand; some beaches in Texas have brown sand; some beaches in Hawaii have black sand. The color of the sand depends on the beach.