I’ve been trying to understand how this system works the entire expansion so far and I still have no idea. I didn’t understand how the upgrade system worked in Dragonflight, either, honestly.
I just go to the item upgrade NPC and upgrade whatever I can and that’s about it. I have no idea how this system works at all, even when I’ve tried to read like WoWhead articles and stuff about it. I just can’t wrap my head around it at all.
That is not entirely your fault, it’s not actually explained in-game (or at least, I can’t remember it being explained). There are different tiers of crests that you can use to upgrade corresponding “tracks” of gear. The lower level crests can be obtained from some solo activities. As you do mythic plus, and start doing higher mythic plus, you begin seeing higher tiers of crests. Right now the highest tier of crest is called Gilded and you can get it from completing a +8. Those will be used for part of upgrading Heroic track gear, and for upgrading Mythic track gear. Up until +7 keys you will get Runed crests which are used for upgrading the first portion of Heroic track gear and the track of gear below that. You also do get some crests from raiding but I don’t recall exactly how those are divvied up by boss. Someone else can do a much better job of explaining it. I always personally had an easier time remembering the top tiers of crests and gear and working my way backwards because in that way I know what I’m upgrading towards, if that makes sense.
Crests upgrade the ilvl of an item, as well as the slot it is attached to. There are 4 crest types, one for each ilvl band for the 4 raid difficulties.
LFR, Weathered 584-593
Normal, Carved 597-606
Heroic, Runed 610-619
Mythic, Gilded 623-639
Once you have an item at that ilvl, you no longer need to spend crests to get a differet item on that slot to that same ilvl. So if you have say 606 shoulders, and you get different shoulders with better stats at 597, you can upgrade them to 606 without spending crests.
The tldr is really to just spend crests as and when you get them, with the exception of not if you expect to almost immediately replace the item with something of an already higher ilvl.