The term 'meme' first appeared in the book "The Selfish Gene" by Richard Dawkins (who coined the term) in 1976. So, 20th century, not 21st. It means a unit of cultural expression, spread by imitation, so a particular religion would be a meme, as would the idea of agriculture, or the bible. It could also be particular turns of phrase which gain popularity by repetition, such as "There are more things in heaven and earth than are dreamed of in your philosophy" or "I'll be back".

I suspect, by the OP's reference to the 21st century, that s/he means something like the "Kilroy was here" graffiti from WW2, but yes, memes have existed throughout human history. The term has only existed since 1976.