The Delayed Exchange Variation is a very clever idea for White. You sacrifice a tempo for a crucial positional gain. Compare the position in the Exchange Variation after 4.Bxc6 with the position here in the diagram after 4.Ba4 Nf6 5.Bxc6. What is the difference?
The difference is in the Delayed Exchange Black's Kingside Knight has been developed to f6. Doesn't this make White worse than in the Exchange Variation?
No because in addition to the structural damage to Black's pawn shell, his Knight is actually poorly placed on f6. It blocks in his f-pawn and this pawn break ...f5 is a thematic option in the Exchange lines.
This gives you ample time to castle Queenside and post your pieces on the Kingside. Your pawns give great cover so you can maneuver at leisure. Your two main plans are to create a pawn majority for the endgame or get a Kingside attack going for the middlegame. If you're Black wait for White to show his hand before deciding what to do with your King.