Exchanging on d5 in queen's gambit like openings I'm  ~2170 rated but having avoided d4 d5 type setups my entire chess career, as some things are quite mysterious to me.
In positions where white has pawns on d4 and c4 and black has one on d5 (typically accompanied by some on c6 or e6, or both), I've noticed that white often exchanges with cxd5 and the reasons behind this are quite enigmatic for me. Often by doing so, white allows black's light square bishop to come out, if not immediately then, in the future. For example, some people will play 1. d4 d5 2. c4 e6 3. Nc3 Nf6 4. cxd5, or similar positions. The exchange may be featured in other positions, for example where black has played b6. Perhaps it's done in the Catalan. Some positions are obvious to me, like in the mainline of Grunfeld's where the exchange leads to a white center. However, often to me it seems that the exchange helps black in regards to piece activity. I suppose the exchange of a side pawn with a center pawn is an argument, but it seems quite soft and unsatisfying. Also, the timing of the exchange also is enigmatic. Could the exchange have happened a turn before, and why precisely now? There are many classical queen pawn openings where this exchange is featured and I would like if someone could explain to me the typical reasons for doing this exchange.
Your incomprehension is very understandable. Black opens with d5 and e6 entombing the light squared bishop only for white to play cd allowing the reply ed from black and, hey presto! the bishop is free! Is white really so stupid? What's the trick?
Well, some white players want the structure that arises, the so called &quot;Carlsbad structure&quot; and they want to pursue the &quot;minority attack&quot;.
Here is the pawn structure:
[fen &quot;8/pp3ppp/2p5/3p4/3P4/4P3/PP3PPP/8 w - - 0 1&quot;] 

The basic idea is that white will advance the a and b pawns and exchange them for black's a and b pawns leaving a weak backward c pawn and a hole on c5 where white can park a piece. The long term aim is to win this weak pawn and end up in a winning ending a pawn up. QED
Of course life isn't that simple. Nevertheless the minority attack is a template which strong players (over 2000) should know. It can occur in a number of openings, not just the QGD. For instance it also occurs, with colours reversed, in the Caro Kann.
There is actually an English GM, Keith Arkell, who has this as one of his main weapons. He is an expert in the kind of endgames which can arise from this opening and the endgame is where he applies most of his effort. (He is also probably the leading expert on the KRB vs KR endgame. Although a theoretical draw he has won something like 95% of the games where he has had the extra bishop.)
He has just published a book, &quot;Arkell's Endings&quot;, which describes his chess philosophy and gives a lot of annotated games showing his methods. The main English chess magazine just published an extract dealing with this topic and including a game. The full article is about half way through this pdf.
Here are some of Arkell's comments and the game:

I rarely look to create unfathomable complications, I don’t carry around an armoury of opening traps, and I don’t concern myself with trying to force a win from the earliest stages. Instead, my opening repertoire and subsequent play are all about creating a framework from which I can try to acquire the tiniest of advantages, and then, inch by inch, convert that into something tangible. Unsurprisingly, I win many of my games in the ending. Very often I am not sure at what point my opponent’s position has deteriorated from what was difficult but tenable, to a forced loss.

Here is the game where Arkell demonstrates his use of the Carlsbad structure as a framework from which he extracts a win.
[Title &quot;Arkell - Bradbury, EACU Open, Newmarket 2019, QGD&quot;]
[fen &quot;&quot;]

1. Nf3 Nf6 2. c4 e6 3. Nc3 d5 4. cxd5 exd5 5. d4 c6 6. Bg5 Bf5 7. e3 Nbd7 8. Bd3 Bxd3 9. Qxd3 {Theory dismisses this position as about equal, or at best only very slightly better for White, but my familiarity with the arising structures gives me a good chance to gain the upper hand} 9...Be7 10. O-O h6 {Normally Black would castle here, but now, by capturing on f6, I would be able to follow up with either 12 Ne5 or 12 b4} 11. Bxf6 Nxf6 12. Ne5 O-O 13. Qf5 {This doesn’t look very ambitious, but I am playing for an endgame in which I can probe on the queenside without having to worry about counterplay} 13...Qc8 14. Qxc8 Raxc8 {My opponent doesn’t make any serious mistakes in this game, but this felt like a minor one since the action will most likely take place on the a-, b- and c-files, so the other recapture was likely preferable.} 15. Rfc1 Bd6 16. Nd3 Rfe8 17. b4 Nd7 { I had calculated 17...Ne4 18. Nxe4 dxe4 19. Nc5 b6 (or 19...Bxc5 20. Rxc5 when b4-b5 will follow, with overwhelming positional pressure) 20 Na6 with the plan of attacking Black’s c-pawn.} 18. a4 {I wasn’t sure about the consequences of 18. b5 c5 19. Nxd5 cxd4 20. exd4 Rxc1 21. Rxc1 and then something like 21...Re2. I’m a pawn up, but it all looks a bit loose, so instead I formulated a plan to fix c6 as a longterm weakness.} 18...Nb6 19. a5 Nc4 20. b5 {Threatening to undermine Black’s whole queenside with a5-a6, so more or less forcing the following sequence} 20...a6 21. bxa6 bxa6 22. Na4 Rb8 {22...Nxa5 23 Nac5 just plays into my hands.} 23. Nac5 Rb5 24. Nxa6 Ra8 25. Nac5 Raxa5 26. Rxa5 Nxa5 {And so we have arrived at base camp – the successful conclusion of the minority attack. I have one pawn island against two; Black has active pieces, so a direct assault against c6 is obviously impossible. The correct procedure therefore is to probe on the kingside in order to inflict a second weakness, or at least to gain some space over there.} 27. g4 { This is by far the best pawn move. If 27 h4 h5 it will be hard to make progress, as breaks with e3-e4 or g2-g4 will involve ruining my own pawn structure} 27...Nc4 28. Kg2 Kf8 29. h4 Ke7 30. h5 { Not only does this move fix a target on g7, but experience of playing these kinds of positions, literally hundreds of times, has taught me that there are certain mating nets Black needs to be wary of.} 30...Nb2 {I felt this was a little impatient, enabling me to activate my rook. It was better to sit tight and await events.} 31. Ra1 Nxd3 32. Ra7+ Kf6 33. Nxd3 Rb3 34. Ne1 Rb6 { Neil played this quite quickly, but I wasn’t sure whether he should be playing 34...c5 instead. Actually I had a similar game at Harrogate about four months earlier where I managed to win from the structure which would have arisen after ...c5.} 35. Nf3 Bb8 36. Rd7 Ke6 37. Rd8 {My opponent’s position has rapidly become critical. I now threaten 38. Re8+ Kf6 39. Ne5 when he will either be mated or face heavy material losses.} 37...Bd6 38. Rc8 {This was a bit lazy. As soon as I had released the rook, I regretted not playing 38. Re8+.} 38...Kf6 {There was a chance to prolong the game with 38...f5, but I could still keep up the pressure with 39 g5} 39. Nh4 { After this move, heading for f5, I could no longer see any way for Neil to avoid losing material. His c-pawn, g-pawn, bishop, and even his king have come under increasing pressure, all because his pieces were tied down to the defence of the c6-pawn – a product of White’s typical minority attack in the Carlsbad structure} 39...g6 40. hxg6 fxg6 41. Rg8 Kf7 42. Rxg6 Bf8 43. Kf3 Ra6 44. g5 hxg5 45. Rxg5 Ra2 46. Rf5+ Ke8 47. Ng6 Bd6 48. Rh5 {I have to be careful to prevent the break ...c5 at a moment when the d-pawn is safe from capture.} 48...Kd7 49. Nh4 Bb4 50. Rh7+ Ke6 51. Ng6 Rc2 { I was pleased to see this as it enables my knight to reach its ideal post, back on d3. On 51...Bd6 I intended 52 Rh6 when only an engine might be able to hang on.} 52. Nf4+ Kd6 53. Nd3 Rc4 54. Rb7 c5 55. Rb6+ Kc7 56. dxc5 Bxc5 57. Rb5 {Either Black enters a lost king and pawn endgame, or he loses the d-pawn} 1-0 

A masterclass from an expert on the Carlsbad structure.