CR is just a mechanical abstraction that doesn't exist in-universe
The CR of a given creature (a.k.a. "monster", but creature is perhaps a more generic term that sounds better for, say, a human NPC) doesn't actually tell us anything about the creature with regards to the narrative. There are other terms we use: HP, AC, XP; these terms also do not exist in-game. PCs and NPCs won't know what "HP" is. HP has an in-game description, as explained further in this question: What does HP represent?
In short, from the PHB, pg. 196:
Hit points represent a combination of physical and mental durability, the will to live, and luck.
So those are things that a PC/NPC might know about and understand; luck, the will to live, etc. They make sense in-game and are something that PCs/NPCs could talk about in-game.
However, CR doesn't even have that; it is simply a way to quantify roughly how difficult a given creature would be to defeat given it's HP, AC, abilities, etc. How that makes sense in the narrative is up to you, the DM, to decide.
Taking two examples, let's compare the Veteran and the Champion. The Veteran is a CR 3 warrior from the Monster Manual, whereas the Champion is a CR 9 warrior from Volo's Guide to Monsters. Both are just NPCs and both appear to fight like warriors (judging by their stats). The only difference between them are things that don't make any sense in-universe; their stats. Veterans only do 2 attacks via Multiattack, whereas Champions can do 3 attack via Multiattack, and has a few other abilities on top of that (such as Second Wind), as well as having higher AC and HP.
In-universe, you could justify this difference in difficulty by claiming that the Champion has had more training, more experience (I know the other is called a "veteran", but apparently this Champion has more experience), or simply that they are just naturally innately better warriors, even if they're technically not as experienced; you could even take Champion to mean that they are imbued by godly powers or something, and that's why they're more of a challenge than a Veteran. Either way, how you justify why one NPC warrior is better than another is up to you as the DM. The statblocks are just provided so that if you do decide that NPC A is better that NPC B for whatever reason, you have different stats to use for each case.
Another example is something like an Orc. Orcs are ferocious creatures to be feared, and yet they are only CR 1/2. However, other variations of orcs exist, and you could even create your own, coming up with homebrew statblocks for orcs with different training. They're still orcs, just like the CR 1/2 Orc, but their statblock would be different and would come with it's own CR, which you can use for any orcs you have decided for whatever narrative reasons should be more of a challenge than a standard Orc.
Another way to look at this would be to take a strong monsters and weaken it. The Kraken is a powerful creature with a few less powerful variants, but who's to say you couldn't come up with a kraken who isn't Juvenile or Malformed, but simply isn't as strong as the "default Kraken"? It's still a kraken, but it doesn't have as much HP or as many abilities, for whatever narrative reason you want to come up with. The only thing "CR" is interested in is how many abilities, how much HP, etc, and it doesn't care for a narrative explanation.
So, to summarise, CR makes no sense in-universe; it is just a numerical abstraction to help you, the DM, determine how much of a challenge this particular collections of stats and abilities would be (which you assign to whatever in-universe creature you decide would be represented by such stats). The fact that we usually use the Orc stats for an orc is not set in stone (you could even have an orc who uses the Champion stats, if you decided that this particular orc should be that much of a challenge...)