The link krushing gave pretty well answers the question. The way I've always understood it was that a bar = a measure. If you are building a beat in 4/4 then there will be four quarter notes to each measure (or 2 half notes, 8 eighth notes, 16 sixteenths)...when penning lyrics to a song, the lines should fit squarely within the bars when rapped (or sung). I think, and i might be wrong, that a rap "bar" occurs every two measures...usually 2 lines that rhyme...each of the lines should be rapped in the same amount of time, fitting squarely within the measures.
In "The Warning" by Em he says:
"As long as the songs' getting airplay I'm dissing you.
I'm a hair away from getting carried away and getting sued.
I was gonna stop at 16
That was 32
This is 34 bars. We ain't even a third of the way through."
In the above example, "As long as the songs' getting airplay I'm dissing you. I'm a hair away from getting carried away and getting sued" was the 32nd bar. "I was gonna stop at 16. That was 32" was the 33rd bar. And the last part is 34.
If you still don't get it, listen to that song on youtube. Listen to the way em raps some lines faster, some slower, adds pauses between words...all to get it to fit right within the measure. 2 lines, 2 measures, 1 bar. 16 bars is essentially 32 lines. That's it in a simplified sort of way...and I could be wrong, but I think that's about right.