A more thorough explanation:

A declaration under penalty of perjury is a statement of facts or testimony that is accompanied by a declaration that the person making the statement will be found guilty of perjury if the facts declared in the statement are shown to be untrue. This means that if someone lies in their statement, they can be charged with perjury, which is a serious crime.

For example, if someone is testifying in court and they make a statement that they know is false, they can be charged with perjury. To prevent this from happening, the person making the statement will often say something like, "I declare under penalty of perjury that the foregoing is true and correct." This means that they are swearing that what they are saying is true, and if it is not, they can be charged with perjury.

A declaration under penalty of perjury can be a written statement, such as an affidavit. If the statement contains the signed declaration that it is made under the penalties of perjury, it does not need to be verified by oath or affirmation orally before the court. This means that the person making the statement is still subject to the penalties assessed against a person found guilty of perjury if the statement is false.

Overall, a declaration under penalty of perjury is a way to ensure that people are telling the truth when they make a statement or testify in court. It is a serious matter, and anyone who lies under penalty of perjury can face serious consequences.