Jessi, "Drop me a line" was first used in the 17th century. Then it meant "send me a few words in writing." A "line" meant a line of writing. In those days a letter or a message would be delivered directly to the person for whom it was intended. So, the messenger would drop it off* at your home, perhaps hand in to you personally by dropping it in you lap. *drop it off means deliver it. In the modern world "drop me a line" has a more general meaning and could refer to almost any kind of written message: a letter, a telegram or a telephone text message, for example. It can also mean to "call someone on the telephone". Although, that is not the original meaning. I think that is because now some people think "line" means telephone line. Examples: I'll drop you a line when I get to the airport. [ I'll give you a call.] or Lyrics from the song "Drop Me a Line" by the Slycaps. i wanna hear your voice on the phone everyday when i get home i'm home all the time drop me a line Денис

It means send him a short message

It's an informal and more friendly way of saying "Send me a message."

write me a letter

give sb a message