To call something precious is to describe it as highly valued. Think of a gemstone when you call your baby sister precious.
Diamonds, emeralds and rubies are all precious stones and gold and silver are precious metals. If it is something valuable and treasured, it can be called precious too. Fresh water is a precious resource especially in desert countries. Many precious books and painting have been destroyed through fire and war. On a more personal note, guard your memories as they will always be precious to you.