Individual Values (IVs for short) are what make each Pokémon unique, even if they're the same species, caught at the same Level and have the same Nature. On a basic level, you can consider IVs as a measure of a Pokémon's natural talent. Like how in real life, some people are naturally smarter than others, while others may be more athletic.
Each Pokémon has a IV ranging from 0 to 31 for each of the six key stats (HP through Speed). The higher the IV, the better the stat. When encountering Pokémon in the wild or breeding Pokémon, IVs are randomly assigned for each of the Pokémon's stat. This is what causes the individual difference in each Pokémon, hence the term.
By the way, the term "Individual Value" is never used in the games; this is simply a term that fans coined, which has prevailed throughout the generations. Instead, the games call these "innate stats", which isn't wrong per se, but nobody actually calls them that.
The IV Advantage
Just like Natures, knowledge of IVs is completely unnecessary for the main story, so you needn't worry straightaway. However, there may come a time when you'll need to consider optimising your Pokémon's IVs.
You see, at Level 100, IVs contributes to an equivalent boost to the Pokémon's stats. At the far extreme, the difference between a Pokémon with 0 IV in a stat versus 31 IV is 31 stat points, which is a big deal in high level play. Meanwhile, at lower Levels, the contribution from IVs is proportionally smaller.
Like Natures, IVs are fixed when you obtain the Pokémon. However, there are ways to influence the IVs.
When breeding Pokémon, the offspring will inherit 3 random IVs from their parents. Or 5 IVs if one of the parents is holding the Destiny Knot item. By carefully swapping out the parents, you can work your way up until you get offspring with 5 or 6 perfect IVs.
Pokémon obtained in Max Raid Battles can have up to 5 perfect IVs (or 6 if you're lucky) at the highest difficulty. Some gift Pokémon can have 3 or more perfect IVs as well. In fact, the Gigantamax Pikachu and Eevee have 6 perfect IVs, making them great parents!
Introduced in Sun and Moon, you can use Hyper Training to effectively increase your Pokémon's IVs. This can be done once you reach the post-game Battle Tower. However, your Pokémon must be Level 100 and you need to hand over a Bottle Cap for each stat or a gold one for all 6 stats.
To Hyper Train or Not?
Hyper Training is amazing, but should be used as a last resort, like Mints. That's because your Pokémon must be Level 100 (which doesn't take long, but is still a hurdle nonetheless) and Bottle Caps are quite rare/pricey. Also, their effects don't pass down when breeding.
Similar to changing Nature with Mints, Hyper Training should be reserved for Pokémon that you cannot easily get with high IVs (like Legendary mons). Ideally, you should try breeding Pokémon and/or participating in raids to cut down on the Bottle Caps required.
Unfortunately, the only way to precisely evaluate IVs, down to the number, is by using an online IV calculator. Be sure to select one that's compatible with Sword and Shield, as some Pokémon species may have different base stats in earlier games.
Because the effect of IVs is greater at higher Levels, you'll get more accurate readings the higher Level your Pokémon are. Meanwhile Pokémon at low Levels can have a huge spread of possible IVs, making it a chore to narrow down the exact values. Don't even bother using a calculator on a Lv. 1 Pokémon!
Once you reach the post-game, you can obtain the Judge function for your boxes, which can reduce your reliance on IV calculators. To unlock it, you need to reach Rank 4 in Wyndon City's Battle Tower. This shouldn't take too long. If you're not feeling confident, go ahead and use your Legendary Pokémon (Zacian, Zamazenta and/or Eternatus).
After unlocking the Judge function, when you're viewing your boxes, press the + or - Button until the window on the right changes to the correct display. Instead of seeing your Pokémon's stats, you should see a statement like "Decent" or "Pretty Good". The box below should also say something like "Good stats" or "Amazing stats!"
These statements are the game's way of giving you the IV values, in a slightly obtuse way. Thankfully, you only really need to know if your IVs meet the following numbers: 0, 30, or 31. Obviously, 31 is the best, but 30 generally has the same effect (if you don't invest EVs), while 0 Speed is useful for Trick Room and 0 Attack to reduce confusion damage.
The following table explains what the statement next to each stats means:
|Very Good||26 - 29|
|Pretty Good||16 - 25|
|Decent||1 - 15|
Meanwhile, the last statement is related to the total sum of a Pokémon's six IVs. This information is far less useful, but still worth mentioning:
|Statement||IV Total Range|
|Amazing stats!||151 - 186|
|Great stats||121 - 150|
|Good stats||91 - 120|
|OK stats||0 - 90|