To soar means more than just to fly; it means to rise swiftly, to feel the wind slipping below you as you ride it higher, higher, higher. Flying is just moving through the air. Soaring, though, suggests exhilaration, even joy.
Think about the anticipation you feel when you buy a lottery ticket — your hopes soar as you contemplate the possibilities. It's the same wonderful feeling you get when someone you have a crush on notices you, when you land that perfect job, when you hold your child. The word soar comes from the Latin, ex-, which means "out," and aura, meaning "breeze, air," together meaning "out of the air," which is precisely how it feels to soar.