Definition: What is meant by "bishop pair" in this context?

Question

This is a screenshot from a chess.com tutorial.

In the final sentence it says,

White will often gain the bishop pair after 5. a3, with a sharp struggle ahead.

Obviously a3 is the pawn attacking the bishop which is pinning the knight, but I'm missing what "bishop pair" means. Assuming that bishop on b4 is one of the pair, does it mean:

• A pair of bishops, in which case which is the other bishop, and where is the gain?
• The bishop and pinned knight form a pair, which will be traded via Bc3 then bxc3, in which case, again, where is the gain? Black has destroyed the pawn structure, but not gained material. Besides, the text says that white makes the gain, not black.
• The black bishop retreats from the pawn, and somehow white makes a gain from it. In which, please help me see that sequence. Does white gain two bishops?
• Something else? Perhaps "bishop pair" is an idiom?

Answer 1

"Bishop pair" is a chess term indicating you have the pair of bishops - i.e. one bishop covering the light squares and one bishop covering the dark squares. If, after a3, Black plays ...Bxc3 and White responds with bxc3, then Black has lost the bishop pair because they only have one bishop left. Meanwhile, White still has both bishops, so they have the bishop pair.

The bishop pair is in general a small advantage, but it's still an advantage. In particular, you can control every square on the board with one of your two bishops. With only one bishop, there'll always be squares you can't control.

Example:

[FEN "rnb1k2r/1p1p1ppp/4pq2/8/8/3B4/PPP1QPPP/R1B1K2R w KQkq - 0 13"]

White has the Bishop pair, which is a significant advantage in this position because Black has difficulty defending the weak squares on b6, c7, d6, c5, and e5. (Plus bishops are just better than knights in open positions like this one where the center is not blocked by pawns.)

Technical note: it's unclear if two bishops on the same color still counts as the bishop pair. Certainly most of the strategy associated with having the bishop pair does not apply in this case. It's very rare to have two bishops on the same color, as well.