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.
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?