This is a great example for explaining the concept of the bad bishop.
In the center, we see an example of a pawn chain. White has pawns on d4 and e5, and black c6, d5 and (soon) e6. These are pretty immobile (until either side plays some pawn break). White's pawns are on dark squares, black's on white squares.
As a result, black's white squared bishop is called a "bad bishop", because it is blocked by its own pawns that are themselves blocked. White's white squared bishop is similarly called a "good bishop" -- it isn't blocked by his own pawns, can help with pawn breaks at the right moment, et cetera.
Why is it even relevant to mention that this variation manages to bring black's white squared bishop outside of the chain? Because being "inside" or "outside" the pawn chain is only relevant for bad bishops. Black's f8 bishop doesn't care about such things. The French defense is a great defense except for things such as leaving its bad bishop on c8.
White also has a bad bishop, the black squared one on c1. But as white has more space (d4 and e5 vs d5 and e6) and the pawn chain is pointed in the direction the Bc1 moves it is less of a problem, from c1 it will continue to influence far-away squares such as g5. Black's bishop on c8 is just locked in. A way to deal with having less space is to exchange pieces so the lack of space isn't felt as much.
Note that outside the pawn chain, it's still a bad bishop -- there are only a few squares the bishop can safely go to from f5, there is a danger that it will be attacked and chased by pawns. But at least it has more influence there than on c8.
So what would be even better for black's bishop than to merely be outside of the blocked chain? Why, to be exchanged for white's good bishop, of course. Without any further concessions, even.
After 4.Bd3 Bxd3 5.Qxd3 e6, black's opening is a complete success. No bad bishop, white no good bishop, less space but already a piece exchanged. Black has no problems whatsoever.
All that said, chess is an equal game anyway. If white could get even a tiny concession out of black, this might still be a useful idea. 4.h4 is a theoretical line (white threatens to chase the bishop with g4, f3, h5) and then if 4...h5, 5.Bd3 is a main move (the other is 5.c4). The difference with what has gone before is that g5 has now become a nice square for white's own bad bishop, and that is enough of a difference.
1.e4 c6 2.d4 d5 3.e5 Bf5 4.h4 h5 5.Bd3 Bxd3 6.Qxd3 e6 7.Bg5 Qb6 8.Nd2
Is an exciting line that scores well for white.