When you're lovelorn, you feel sad or hopeless about love. Sometimes people are lovelorn when the person they love doesn't love them back.
You could be lovelorn because of unrequited love, loving someone who's unavailable or who simply doesn't feel the same way; or lovelorn from the loss of love. A lovelorn poet might write a melancholy sonnet, and a lovelorn teenager might listen to sad songs and cry in his room. The poet John Milton is often credited with coining lovelorn, a combination of love and lorn, a very old-fashioned way to say "lost" or "ruined."