What Does Senpai Mean?
Senpai (also spelled sempai) can refer to someone you wish to attract your attention to, whether it's someone you admire and want to be friends with or someone you're romantically interested in.
Senpai first appeared in Urban Dictionary in 2004, when a user defined it as "an upperclassman." Since then, other entries (many of which mention anime and manga) have been added, and it's now defined as "someone older than you," "someone you look up to," "mentor," "senior," and a "older person who you adore."
"Someone who will never notice you," says the top definition (as picked by users).
Which is unfortunate, because, as KnowYourMeme points out, it's all about catching senpai's attention. Characters in anime and manga regularly endeavour to win a senpai's love or attention, and words about getting noticed by senpai have become popular catchphrases.