The brain is located in the head, and the idiom to use one's head is based on this simple fact. Using your head is equivalent to thinking, and making use of your brain and the power it has to be careful, consider all the facts and make good decisions in a variety of situations.
Example 1: If we use our heads and create a workable solution, we can survive a really bad situation.
Example 2: I told my son to use his head when he was driving, and he thought I was making a joke - he said he always uses his hands.
Example 3: John didn't use his head when he started the new ad campaign, and it was a failure.
Example 4: Always use your head and pay attention when you are in a new environment or situation, and you will probably be fine.