to confirm that a statement or fact is true
The two Governments affirm their solemn commitment to support, and where appropriate implement, the provisions of the Multi-Party Agreement.
to make a solemn declaration in place of an oath (=a promise that that a person will tell the truth (especially in a court of law), especially one that makes reference to God or to a holy book) by a person who objects to taking an oath for reasons of conscience
The witness chose to affirm rather than swear on a religious text such as the Koran or the Bible.
to officially say that a judgment, decree, or order etc is valid (=acceptable and will be upheld)
The court of appeal affirmed the judgment of the lower court.