Can you use a land's activated ability to produce mana during another player's turn?

Mana abilities are a special category of activated abilities that produce mana as part of their effect. Under CR 605.3a, mana abilities can be activated any time you could play an instant — and in many cases even without requiring priority — meaning you are not restricted to your own turn.

Basic land abilities (e.g., tapping a Forest for green mana) are mana abilities under CR 605.1a. Because they are mana abilities and not spells, they don't use the stack and resolve immediately (CR 605.3b). This makes them extremely flexible — they can be used in response to spells, during combat, or at any point you need mana, even on an opponent's turn.

You do need a reason to be acting on another player's turn. The most common reason is that you have priority (e.g., an opponent cast a spell and you want to cast an instant in response). You tap your land for mana as part of producing the mana needed to pay for that instant. You can also activate mana abilities as part of paying costs even when you wouldn't otherwise have priority (CR 605.3b).

Concrete example: It's your opponent's turn and they cast Lightning Bolt targeting your creature. You want to cast Giant Growth in response. You tap your Forest for green mana (an activated mana ability used on your opponent's turn), then cast Giant Growth. The mana ability resolved instantly without using the stack, and your Giant Growth is placed on the stack above Lightning Bolt.

The only restriction is that lands with non-mana activated abilities (e.g., a land that draws a card) follow normal timing rules and would require you to have priority and to use them at an appropriate time — but that's a different situation from mana abilities specifically.