Your attention might be caught by either of two things, both of which must be seen one way or another. (a) The first is simply that Black’s queen attacks White’s rook on d6, which is guarded only by its fellow rook on d2. (b) The second is that Black has a battery of queen and rook bearing down on e1, almost ready to perform a back rank mate. When you imagine a move like Re1+, a first thought should be to look for anything your opponent can interpose on the back rank between your attacker and his king—and then whether it would have protection to prevent your attacker from just taking it and renewing the threat. In this case Black’s Re1+ is rebutted with Bf1; and Black can’t then just play RxB+ because White’s bishop is guarded by its queen.
So Black has two threats against White—a threatened capture and a mate threat—that are prevented by White pieces guarding the relevant squares. Looking for ways to incapacitate either defender and you are led to Bd3—which at least for the moment blocks the paths of both of them. White can’t afford to let his bishop be cut off from f1, since then Black plays Re1+ and White has no way to stop him from mating (White’s Qf1 is met with RxQ#). But if White does play BxB, his own bishop cuts off the protection of his rook on d6. Black takes it next move, winning the exchange.
The order in which the two initial ideas are seen is not so critical. Your investigation of either threat by itself should lead to Bd3. When you imagine White’s possible recaptures (BxB or RxB) you see that the result in either case is to sever a line, and you look to see what the blockage would make possible.