A "reserved" person is someone who is quiet, doesn't usually state their opinions publicly, and controls their emotions:
My father was always reserved at home, but I used to hear from guys that worked with him that he was the life of the party,
The meaning of "reserved" is similar to "shy", but "reserved" has more of a positive meaning. If you say that someone is "shy", it sounds like they want to be more outgoing, but they're too afraid to. If you say that someone is "reserved", it sounds like they've made a decision to be that way.
"Reserved" is an academic-sounding word, so you might not hear people use it much in casual conversation. Instead, someone might describe a person as being "quiet", "shy", or "even-tempered".