In courts of law in places that respect the separation of church and state, if the court usually asks witnesses to “swear to tell the truth, the whole, truth and nothing but the truth, so help you God,” or some variation thereof, atheists and agnostics might be offered the option of being sworn in by affirmation instead. In an affirmation, they still promise to tell the truth, the whole truth and nothing but the truth, but they’re not required to invoke the name of an invisible being that they believe does not exist, because that would be ridiculous and pointless.
In a similar vein, if there is a situation that calls for you to swear an oath to a monarch or other sovereign, if you conscientiously object because your religion might not allow it or because you think it’s absurd to swear an oath to a hereditary monarch in a democratic society, you might, but not necessarily, instead be offered the option of providing an affirmation in which you promise to do whatever is being asked of you.
In addition, if you affirm that something is true, that statement is an affirmation. You could probably have figured that one out on your own. If not, you need remedial English lessons that are beyond what I can provide.