I see this quite frequently in Japanese, especially on the news. I have some vague impression of what it means, but i'm not really sure.

So basically, what does について　mean?

A context example, taken from NHK today:

"ジャクソンさんの死についてロサンゼルス市警察は記者会見で"

Thank you.

に就いて/ に就く. As a Heisigian you will surely be able to figure it out from the Kanji. "about", "regarding", "concerning". に関して/に関する means basically the same, sounds more formal though.

I always think "with respect to" if I need to translate mentally. Seems to work.

"Regarding" / "about".