You use comparative to show that you are judging something against a previous or different situation. For example, comparative calm is a situation which is calmer than before or calmer than the situation in other places.

A comparative study is a study that involves the comparison of two or more things of the same kind.

In grammar, the comparative form of an adjective or adverb shows that something has more of a quality than something else has. For example, 'bigger' is the comparative form of 'big', and 'more quickly' is the comparative form of 'quickly'.