I don't understand this puzzle solution

I can't wrap my brain around this puzzle.  The correct answer was Re5, taking the bishop.  I fail to see how this does anything besides losing White's rook.  The puzzle ended there, so I wasn't able to see what would come next.

Can someone smarter than me please explain how trading my rook for a bishop makes my position stronger?

So White has an active checkmate threat.  Imagine if your queen was on g7.  That would be checkmate!  How can your queen get there?  It has to go to f6, and f6 has only one thing defending that square: the bishop on e5.

If Black takes your rook on e5, then Qf6 and mate is coming.  Black's best move will then be to f5 to prevent the mate but accept the lost of the bishop.

Now I see it, thanks.  God, I'm bad at this.

it is good because it frees the square which allows white to have a checkmate threat. therefore it is the solution

How? It's whites turn. If white takes the bishop, then what?