Refers to a person from the same country. Can also be used for someone from the same province or region within a country, though less common.
I feel relieved when I meet a fellow countryman abroad.
person from said country
Used when the country is already clear from context, often in contrast to other nationalities.
This shop is run by a person from that country.
Compound of 同 (same) + 国 (country) + 人 (person).