When you woo someone, you are being charming because you think that it will make them love you more. You want to win their heart, so you woo them, you flirty dog you.
Poetry is a great way to woo someone, because who could resist such beautiful words? Wooing requires a romantic heart and a lot of focused attention on the person you desire. But wooing isn’t always just done for love, and you can woo someone because you want their support, like when a rock band woos a record label to release their album, or wooing your grandmother because you need to borrow some money.