1.
doctor, PhD holder
A person who has received a doctoral degree; an academic title.
2.
expert, specialist
A person with extensive knowledge in a particular field; often used colloquially or in nicknames.
Usage: 博士 can refer to (1) an academic doctoral degree holder, or (2) colloquially, an expert in something. The reading はくし is also used in formal/academic contexts.
Common patterns
Academic degrees
Note: In formal academic contexts, 博士 (on-reading) is preferred. 博士 (kun-reading) is more colloquial and used in titles like 「〜博士」.