I'm reading through some of the handbooks on another site and I keep seeing a reference to "buying off" with regard to races. What exactly does this mean?
i kinda guess where you read it 
the "buyoff" is LA-buyoff this is a optional rule from Unearthed Arcana
it can also be found here: www.d20srd.org/srd/variant/races/reducin...
it can be used to reduce the level adjustment of powerful races like for example drow...
rubberduck
The real advantage of using Buy-off is twofold.
(1) ... you get to take utilize Experience Is A River [thread with no link] and come out slightly ahead on the exp curve
(2) ... you get to use regular CO-builds up to level 20, without having to do really complicated math
The math is "simple" in that you get 1.5*exp while you are down a level. So you catch up more quickly each level.
LA+1 catches up by level 10
LA+2 catcher up around level 16 or so.
LA+3 is much more complicated, and involves a debate as to whether you buy-off 1 or 2 or 3 levels.
If you and your DM agree on the math, you are in like Flynn.
I don't really mind the buy off system that much but, I prefer playing lesser races because then you just don't worry at all about the level adjustment. Even though Lesser Aasimar and Lesser Tieflings are somewhat over powered.