"Take On Me" is a song by the Norwegian band A-ha, from their album Hunting High and Low released in 1985, and the lyrics (and title) has been bothering me for the past thirty years or so. The chorus goes something like this:
Take on me (take on me)
Take me on (take on me)
I'll be gone
In a day or two
Now, the phrase "Take on me" sounds very much like a Scandinavianism for lack of a better word. (I don't speak Norwegian but I do speak Swedish. Meh. Close enough.) In Swedish you can translate this word for word:
Take – Ta (or: Tag)
On – På
Me – Mig
What you end up with is "Ta på mig", which means touch me. It looks as if they just translated the Norwegian equivalent of touch me, word for word, and ended up with take on me. This would make sense, thematically.
Best Answer
It's a music lyric and hence has some liberty.
But "take on" is a fairly common idiom in several contexts. It can mean "engage in combat", but a less aggressive meaning is to accept some burden or responsibility. Google finds "she didn't want to take on more responsibilities", "why would I want to take on an apprentice", "why did I want to take on the role as a GM", "I want to take on Usain Bolt's legacy", "does someone want to take on this project".
"Take on me" can thus be considered to be a plea for "you" to take on the burdens and responsibilities of having a relationship with "me". Or it can simply be considered a poetic rewording of "take me on" (which can itself be interpreted in a number of ways).