A more thorough explanation:

Definition: To state solemnly or positively; to aver.

Example: The witness asseverated that he saw the defendant at the scene of the crime.

Explanation: In this example, the witness is making a solemn and positive statement about what he saw. He is not just suggesting or implying that he saw the defendant, but he is stating it as a fact. This is what it means to asseverate.

Related term: Asseveration - a solemn or positive statement or declaration.