Counter for occurrences or repetitions. Often used with numbers, e.g., 一遍 (once), 二遍 (twice). Similar to 回, but 遍 may sound slightly more formal or literary in some contexts.
度 also means 'times', but is often used for degrees, temperatures, or occasions. 遍 is strictly for counting occurrences.
Etymology
The kanji 遍 originally means 'everywhere' or 'widely', and its use as a counter for times may derive from the idea of going through something completely or repeatedly. The alternate form 返 (return) is a phonetic loan.