UR is an abbreviation used for Unlock Reality a term which signifies something deep or wise. UR is Unlock Reality

Big Up is a show of respect.

Hense, a UR-Big-Up is a show of respect for something or someone showing depth or wisdom.

These have begun to appear especially on Myspace as comments which start with:

Unlock Reality (UR) followed by a greeting

i.e.
Unlock Reality (UR) Cool!
Unlock Reality (UR) FUN!
Unlock Reality (UR) Fantastic!
Unlock Reality (UR) the one!

If you receive a message like this with a good term at the end, you may feel highly complimented as you have received a UR-Big-Up, indicating that the sender sees you as part of the solution to world problems and not part of the cause.