期限（きげん） means a time limit, due date, or expiration date. It focuses on the point when something must be done, or when something stops being valid.
Common uses include 期限を守る（きげんをまもる） for meet a deadline and 期限が切れる（きげんがきれる） for expire or run out of time.
A very common compound is 有効期限（ゆうこうきげん）, meaning period of validity or expiration date. You see it on things like credit cards, passports, coupons, and licenses.
Be careful with 締め切り（しめきり）. Use 締め切り for submission deadlines, such as applications, homework, or forms. Use 期限 more broadly for validity limits and time limits, especially when something becomes invalid after that point.