Here are some examples:
* Monk (general term, not capitalized)
* Brother Thomas, a Franciscan monk (formal title, capitalized)
* The Benedictine monks of Monte Cassino (religious order, capitalized)
However, you don't capitalize "monk" when it's used as a general noun or a descriptive term:
* The monk was meditating in the garden.
* She was known for her monkish lifestyle.
So, it depends on the context!