A reserved person keeps their feelings to themselves. They answer your questions, they are perfectly polite, and after an hour you still know nothing about them.
Reserved is not shy and not cold: shyness is fear, coldness is dislike, and reserve is a decision about what to show. In British English it sits close to a compliment. The word has a separate everyday life as well — a reserved table, a reserved seat on a train, the little card that says RESERVED, and 'all rights reserved' at the front of a book. The noun reserve does both jobs: money held in reserve, and 'she has a certain reserve', meaning she holds herself back. The mistake to avoid is calling someone reserved when you mean rude; reserved people are quiet, not unkind.
1adjectivereservedNot showing feelings or talking about yourself.
“Her father was a reserved man who never raised his voice.”
synonyms: undemonstrative, private
2adjectiveparticularKept for a particular person or purpose.
“The front row is reserved for family.”
3adjectivegivenKept back and not given away, said of rights or powers.
“All rights reserved by the publisher.”