Can you play a land during a turn you took an extra turn?

Extra turns are complete, normal turns that follow all standard turn structure rules. Nothing about an extra turn restricts your ability to play lands — you still get one land play per turn by default, as stated in CR 305.2: 'A player may play a land any time they have priority and the stack is empty during their main phase, as long as they haven't played a land this turn.'

The key point is that your land-play count resets each turn. When an extra turn begins, you start fresh with zero lands played that turn. So yes, you may play a land during an extra turn just as you would on any other turn.

If multiple effects grant you additional land plays (e.g., Exploration or Oracle of Mul Daya), those apply on extra turns as well, since those effects typically say 'each turn' or 'per turn' and an extra turn qualifies as a turn.

Concrete example: You cast Time Walk, giving you an extra turn. At the start of that extra turn, you draw a card, then during your main phase you play a Forest from your hand. This is perfectly legal — it is your one land play for that extra turn.

Relevant rules: CR 305.2 governs land plays per turn, and CR 500.7 confirms that extra turns proceed normally through all phases and steps unless specified otherwise.