Can someone explain to me the ideas behind a4 in the Ruy Lopez?  Around moves 8-10, after black has played a6 and b5 putting whites light bishop on b3, the move a4 starts showing up in games explorer with strong resutlts for white.  I am interested in this move, but I do not understand it at all.  What is it trying to accomplish?

At move 8, a4 is usually to avoid the Marshall Gambit after 8 c3 d5.  It is rarely seen at move 9 or 10 in the main lines, but the positional idea is the same:  White attempts to disrupt Black's plans on the Queenside before proceeding with his own designs on the Kingside. 

It's not considered critically challenging for Black, and is most often seen at move 8 just to duck the Marshall.  Not that White hasn't notched some great wins with the line, it's just that they weren't a direct consequence of the opening or a2-a4.

It's a mainline in the Zaitsev variation(chessgames.com opening explorer):

1. e4 e5   2. Nf3 Nc6   3. Bb5 a6   4. Ba4 Nf6   5. O-O Be7   6. Re1 b5   7. Bb3 d6   8. c3 O-O   9. h3 Bb7   10. d4 Re8   11. Nbd2 Bf8   12. a4

and in the Breyer variation:

1. e4 e5   2. Nf3 Nc6   3. Bb5 a6   4. Ba4 Nf6   5. O-O Be7   6. Re1 b5   7. Bb3 d6   8. c3 O-O   9. h3 Nb8   10. d4 Nbd7   11. Nbd2 Bb7   12. Bc2 Re8   13. Nf1 Bf8   14. Ng3 g6   15. a4

The move a4 is certainly a very typical idea in Ruy after black has played b5. Of course each concrete position has it's own pecularities but it's often a usefull move for white because: a) he may sometimes be able to attack against the b5-pawn and b) white gains the possibility to activate the a1 rook by opening the a-file with axb5 (of course this file would also be open for black but white's advantage lies in the fact that he can decide when to open the file). If black, on the other hand, replies a4 with b4 then white for example gains the c4-square and if he has time for a5 then a6 might also be weak whereas bxa4 by black leads to more pawn islands.

The point behind the a4 also gives a nice square for the white bishop to move if the pawns are exchanged and it also prevents blacks bishop or knight to go to a4. I believe that it's a very useful and challenging move that black has to look at very carefully.