To assert is to state something positively and often forcefully, or to compel recognition of a right, a claim, or an authority by exercising it rather than merely announcing it.
The verbal sense carries a specific weight: an assertion is offered on the speaker's confidence, not on evidence. This is why journalists write that a source asserted something when they mean to report the statement without endorsing it, and why assert sits differently from affirm (to confirm what is already established), aver (to state as verified fact), and declare (to state formally and publicly). The second sense is not verbal at all. To assert authority, dominance, or a territorial claim is to act in a way that makes its existence undeniable, which is the family the reflexive assert oneself belongs to — attested from 1879 and meaning to stand on one's rights rather than to talk about them.
The word entered English around 1600 from Latin assertus, past participle of asserere, "to lay claim to, appropriate," built from ad ("to") and serere ("to join together, put in a row"). In Roman law asserere named the physical act of laying a hand on a person to declare them free or enslaved — a claim made by gesture, not speech, which explains why the non-verbal sense sits so naturally beside the verbal one.
An assertion is not an 📝axiom: an axiom is granted as self-evident and needs no defending, while an assertion is advanced by someone and can be contested. And asserting 📝authority is distinct from holding it — the word names the act of pressing a claim, not the standing that makes the claim good.