Drew Hardwick is an ex-boyfriend of Taylor's from her debut/highschool era. Drew was the inspiration for many of the songs on her self titled (Debut) album. Taylor wrote his name explicitly into Teardrops On My Guitar, in which he responded with getting a car sticker that said 'Taylor Swift wrote a song about me' and he reportedly showed up two years after Teardrops On My Guitar was released at Taylors doorstep, saying, "Hey, how's it going?" with Taylor responding, "Wow, you're late?". In 2015, Drew was arrested alongside his wife and friend for child abuse. (ouch) No further information was to be found regarding his arrest. Drew is believed to be happily married now with no bad terms with Taylor, however theres no confirmation, since Drew is not a public figure.
It’s been speculated that this song was written for Drew when he was a senior dating Taylor who was a freshman at the time, and how she wanted him to remember their times together before he went off to college
Drew’s name is explicitly mentioned multiple times in the song- and back in 2006-ish Drew confirmed that he was the boy Taylor dated and wrote the song about (even getting a custom license plate/bumper sticker saying “Taylor Swift wrote a song about me”)