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[fen ""]
1. d4 d5 2. c4 c6 3. Nc3 Nf6 4. cxd5 cxd5 5. Bf4 Nc6 6. e3 a6

I do not see the point of this move. At first I thought it is aimed to prevent Bb5 and thus maintain the knight on c6, which controls e5, a square where White has a firm grip. It also prevents Nb5-c7, which is not yet a threat but might very well become one, as the White bishop is aiming at c7.

But after checking those threats aren't real and even if ...a6 is not played, in most continuations the best move for White is Bd3. Meanwhile the move ...a6 actually creates responsibilities (I would not yet say weaknesses, but work is required to avoid them) for Black, mainly because the advance ...b6 to control c5 leaves the queenside vulnerable (as demonstrated in Kramnik - Aronian 2012)

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It prevents Nb5-c7. That's the main point behind the move. Just take a look at the disaster a careless move like 6...g6? could lead to.

6...a6 is not the only option, though. Black can try for instance 6...Bf5 (which is indeed more popular), intending to reply to 7.Nb5 with 7...Rc8. 6..e6 is another common move.

A good reason to prefer 6...a6 could be flexibility. 6...e6 makes it hard for the c8 bishop to find a good diagonal. 6...Bf5 could run into trouble against some Qb3

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    That was my first guess as well but 6...g6 isn't a blunder; after 7. Nb5 Black has counterthreats e.g. 7...Qa5+ (which could lose White castling rights) or 7...e5 8. Bxe5 Nxe5 9. Bxe5 Ne4 threatening Bb4+. – Allure Oct 13 '20 at 20:25
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    "6...Bf5 could run into trouble against some Qb3" Can you expand on this? 6...a6 does give black additional options to deal with Qb3, for example Ra7 or b5, so maybe countering Qb3 idea is the main purpose of 6...a6? (Just to clear, I understand that Qb3 is not a threat when the bishop is still on c8, but a6 prepares development of the bishop, for example 6...a6 7. Bd3 Bg4 8. Qb3 is not a big threat). – Akavall Oct 13 '20 at 21:02
  • @Akavall As you said, with a bishop on c8, Qb3 is a non-threat. After the bishop moves, if at least you have the pawn on a6, you can sometimes reply ...b5 to Qb3 – David Oct 14 '20 at 7:14
  • OK I really underestimated how good of a reply White has to 7...e5. White has to be precise but comes out on top within a few moves. – B.Swan Oct 14 '20 at 10:58

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