Mastery is the term used for Warframe experience. As a player levels up different Warframes and weapons, it earns Mastery towards their total player level. For every level a weapon gains, it will provide the player with 100 points, and 200 for Warframes, Companions and Archwings.
However, an item can only count towards Mastery once. If it is reset using polarization, or a second identical item is bought, it will not count towards Mastery points.
Leveling up Mastery has benefits for the players. Some weapons that are more powerful are Mastery Locked, and require the player to reach a certain level before they can be used, or crafted. Increasing mastery rank will also increase the number of premade loadouts, number of extractors a player can deploy, and the maximum reputation one can earn with a Syndicate.
In order to learn more about Mastery and the various tests players need to pass to unlock higher ranks, please refer to this WIKI article.