Can you cast a spell using mana from Selvala Explorer Returned that was produced during an opponent's turn?

Mana does not persist between steps, phases, or turns by default. According to CR 106.4, mana that remains in a player's mana pool at the end of a step or phase is lost (with certain exceptions, like the 'mana burn' rules of old, which no longer exist, but the emptying still occurs).

Selvala, Explorer Returned's activated ability produces mana for each player. If this ability is activated during an opponent's turn — for example, during their main phase — any mana you gain goes into your mana pool. However, that mana empties at the end of the current step or phase (CR 106.4). It does not carry over to a future phase, step, or turn.

The only exceptions to this emptying rule involve cards that specifically say mana 'doesn't empty' at a certain time, such as Omnath, Locus of Mana. Selvala, Explorer Returned grants no such exception, so the mana is lost if not used immediately within the same step or phase.

Example: An opponent activates Selvala during their first main phase. You receive 2 green mana. If you don't spend it before their first main phase ends, it empties from your mana pool. You cannot hold it to cast a spell on your own turn.

Therefore, while you can certainly respond to Selvala's activation and spend the mana during that same phase (e.g., casting an instant), you cannot save it for a future turn.