Andy:
"Buying the Button" means that this player is posting BOTH the small and big blinds (for the current hand).
Let me give you an example:
Last Hand --
Seat 1 is the buttoin
Seat 2 is the SB
Seat 3 is the BB
Seat 4 is the UTG, etc.,etc.,
Seat 4 goes all in
It is folded around to Seat 3, the BB who calls the all in, Seat 4 has Seat 3 covered. The hand plays out and Seat 3 is busted and leaves the table.
Next Hand --
Seat 2 is the button
Seat 3 is vacant, but a new player has been assigned and is on his way to the table
Seat 4 posts the BB, etc, etc.
Upon arrival, before the dealer starts dealing any cards, the new player in Seat 3 announces he wants to "Buy the Button". The dealer says you have to post both blinds and the player says OK and does so. Seat 4 pulls his BB back. Seat 2 is still the button, Seat 3 posts both blinds and Seat 4 is now the UTG. The hand plays out.
Next Hand --
Seat 3 is the button
Seat 4 is the SB
Seat 5 is the BB
I hope this clears things up for you.