Use the adjective significant to describe something that is important. Your "significant other" means the person who's most important in your life. A significant result in a scientific study is a result large enough to matter.
A less common meaning of significant is to describe something that has a special or hidden meaning. A significant smile can convey feelings or information without words. This adjective is from Latin significans, from significare "to signify," from signum "a sign, mark" plus facere "to make."