In American English, master’s degree is usually lowercase when used in a general sense. She earned a master’s degree in history is the standard form.
Capitalize it when it is part of a formal degree name. Master of Arts in History takes capitals because it is a proper title. The same applies on resumes and diplomas where the full formal name appears.
Style guides differ on edge cases. The Associated Press stylebook generally keeps academic degrees lowercase in running text, while the Chicago Manual of Style capitalizes formal degree titles. When writing for a school or employer, follow their house style.
A simple rule covers most cases. Generic mention, lowercase. Full official title, capitalize. Related: when a master’s degree is capitalized, when to capitalize master’s degree, and capitalizing master’s degree in a sentence.

