Casual: も may be dropped → [verb て-form] + いい
Permission question: ~てもいいですか
The structure ~てもいい is used to express or ask for permission. It conveys that something is allowed or acceptable – similar to "may," "it's okay to," or "you can" in English.
When used in a statement, ~てもいい indicates that an action is permitted.
When used with か (or rising intonation in casual speech), ~てもいい becomes a polite way to ask whether something is allowed.
A common response to grant permission is どうぞ ("go ahead") or いいですよ ("sure"). To deny permission, ~てはいけない or ~てはだめ ("you must not") is used.
In practice a flat refusal is often avoided. Trailing off is the usual polite way out:
~てもいい literally breaks down as the て-form + も ("even") + いい ("good"), so the underlying meaning is "even if you do ~, it's fine." This explains why it naturally conveys permission. In casual speech, いい can be replaced with だいじょうぶ大丈夫 for a softer tone: