A conservatory is normally characterized by the following:
A building largely made up out of framing and glass panels.
A building that has been made with an eye for design or looks.
A building which main purpose is as a living / activity space for people.
A building that is often (but not always) attached to a house or other type of building.
A building that has a glass roof and one or more glass wall.
A building that often has plants but also has other objects like furniture (that looks like it is supposed to be there).
A building used for things like enjoying the sun wile isolated for the cold outside air.
This is in contrast with a greenhouse, a building that is often confused with a conservatory as the main purpose of a greenhouse is the growing of and the caring for plants.
A few examples for a conservatory are the following:
A swimming pool with a glass roof and wall(s).
A room in a house or attached to a house with furniture for seating and more which may also have some plants.
A free-standing building in a garden like you sometimes see in anime or high society series where they are drinking tea.
A botanical garden can also be called a conservatory although it often overlaps with a greenhouse.
