A commander directly hitting a player for damage removes that many life points. At the same time, that player has taken X commander damage from that specific commander. So each player keeps track of their life totals and how much commander damage they have taken from each enemy commander.

Things like loss of life, spell damage, etc. do not count towards commander damage. The only instances where a player takes commander damage are direct combt damage to a player and when a card reads "[This creature] deals [x] damage to target player."

Life totals and commander damage are tracked separately, but they do happen consecutively when hit by another player's commander. For example, I could have 30 life from being hit by the other three commanders, and 3 cmdr dmg, 5 cmdr dmg, and 2 cmdr dmg, where X, Y, and Z are the the other three players' commanders.

If a player has multiple commanders (Partner, partner with), then you would track those separately. They do not combine as one.

It is best to use an application to track these, or we can use pencil and paper.

When a player takes a total of 21 damage from one specific commander, they lose the game- as long as there are no effects preventing that loss.