A heart is equivalent to a vote of confidence. Listeners heart songs they like as a way to express their love for it. Just click on the heart shaped button on the right hand side of each song to show your love. Every day, you're given an allowance of hearts for voting on songs. Each heart corresponds to a vote, and your daily heart allowance resets every 24 hours. The formula for the number of hearts you get per day is currently 9 + (your current level).
After you reach level 5, you can heart a song more than once: up to the amount your level is, this is called 'max hearting'. E.g. a level 5 can heart any song up to five times, a level 10 up to ten times, etc.