Counter
Counters are abstract numbers that are associated with face-up cards on the battlefield. They are typically represented by putting a die with the desired number on top of the card, color-coded to the type of counter.
There are two main types of counters:
- Damage Counters, that represents damage (combat or effect) sustained by a creature during the game and can lead to its destruction
- Mana Counters, that represent the current amount of mana a card possesses that can be spent by its controller (usually acquired when the card is summoned)
All counters are persistent, meaning the stay on the card as it moves around, but cease to exist if the card is no longer face-up on the battlefield. Counters cannot exist on cards anywhere else in the game.
There are however other less common types of "counters"; for example, when using the Reap action, you are allowed to collect Souls in cards on the field, similar to other types of counters.
There is no generic "counters matter" effects, so it doesn't really matter what kinds of things are defined as counters (this term is just to facilitate game understanding).