Believe is a verb that refers to accepting something as the truth. It is a stative verb that refers to a state rather than an action. It can also refer to having religious faith.
Believe sometimes is used as a synonym for think. Like in this sentence: I believe she was here some time back.
Belief is a noun. It refers to the act of accepting something as the truth. It refers to accepting something without proof and evidence. We use the word belief when talking about, faith, confidence, and trust.
Belief is also used to refer to a strong opinion or conviction. Like in this sentence: His belief in his theory grew stronger with experience.
The main difference between belief and believe is that belief is a noun and believe is a verb.