a6 here leads up to b5, but still... I see this move played in a lot of endgames in which there is no consequent pawn push. Is it just to control territory (i.e. the 4 squares that the pawn duo controls?) Also, black's move h6 prevents g5, but is that all it does? Is it really worth wasting a move to prevent white from moving g5?

I think 15...h6 has two purposes - one is to clamp down on the g5 square, as otherwise White will play g5 cramping Black's play on that side of the board - Black's king will no longer be able to access the f6 square. The other purpose is to blunt the attack of White's rook on the h-file, which allows Black's h8-rook to pursue other goals on the queenside.

As for 16...a6, I believe the point is to prepare ...b5 in response to the threat of b4. If Black played something else, say 16...Rhb8, then 17.b4 a6 and now 18.a4 looks strong to me. With 16...a6, Black is prepared to meet 17.b4 with 17...b5 with ...Rhb8 and ...a5 to follow. If 18.c5 then 18...a5 and Black will likely end up controlling the a-file.

interesting text:

Ukranian-German grandmaster Efim Bogoljubow (left, 1889-1952) was one of the strongest players in the world from the mid-20s through at least the early 30s, twice playing Alexander Alekhine for the world championship. He was unsuccessful on both occasions, but the fact that he twice contended says something about his strength. He won the major tournament in Moscow 1925 ahead of Emanuel Lasker and the then-world champion, José Raúl Capablanca (picture below), and won many other tournaments as well.

As I said, he defeated Capablanca (1888-1942) in that tournament, and in the tournament book for Moscow 1925 wrote the following: "Further, it is apparent that Capablanca finds it very difficult to separate himself from his dry style of play. His technique, on the other hand, has been at least equalled by Bogoljubow and is not especially feared by the other masters." Pretty cocky fellow, that Bogoljubow. Yes, he had won a prestigious event, but Capablanca was the world champion and lauded as an all-time great. Further, Capablanca had beaten "Bogo" in their individual game in the tournament, so a bit more humility might have been in order. At any rate, I imagine that everyone reading this knows what happened in their next game.

It took a while to occur, as tournaments were rarer in those days, but they next met in Bad Kissingen 1928. Capablanca had lost his crown to Alekhine the year before, and Bogoljubow's star was still on the rise – he would play his first match with Alekhine a year later. In fact, to Bogoljubow's credit, he won the tournament. In round nine, though, his game with Capablanca went exactly according to the script. They very quickly reached an endgame, one that started with Bogoljubow enjoying at least equality, and from that point on he was completely and brutally outplayed. On move 20, he was equal or possibly a touch better; by move 32, he was simply lost, and without having made any outright blunders.