To tap a land for mana is to activate one of that land’s mana abilities that has {T} in its activation cost and produces mana as it resolves.

The ability will trigger each time a nonbasic land is tapped for mana. Each of these abilities goes on the stack and resolves separately.

If any nonbasic lands are tapped for mana while a player is casting a spell or activating an ability, Burning Earth’s ability will trigger that many times and wait. When the player finishes casting that spell or activating that ability, Burning Earth’s triggered abilities are put on the stack on top of it. Burning Earth’s abilities will resolve first.

On the other hand, a player can tap nonbasic lands for mana, put the Burning Earth triggered abilities on the stack, and then respond to those abilities by casting an instant spell or activating an ability using that mana. In that case, the instant spell or activated ability will resolve first.