What Does "Under Oath" Mean?
An "oath" (sometimes called an affirmation) is a formal promise used to confirm that certain information is true (i.e. based on a person's personal knowledge or belief).
To swear an Affidavit under oath means you've made a promise that the information in your document is true. The consequence for lying while under oath is perjury.
"Perjury" is a criminal offense that involves deliberately making untrue statements after making an oath. It can result in hefty fines or jail time.