All Pokémon have a Nature, which reflects their personality and also slightly influences how they fare in battle. Natures are randomly assigned and you can directly identify a Pokémon's Nature by going to the 4th tab of their status screen.
There are a total of 25 possible Natures, each boosting a particular stat by 10% and lowering another stat by 10%. This is also shown on the Pokémon's stat display--a red stat indicates a boost, while a blue stat indicates a drop. Or if the same stat is increased and lowered, you won't see a difference.
Below is a chart that describes every Nature. Besides affecting a Pokémon's stats, Nature also determines what flavours of curry a Pokémon likes or dislikes.
Taking Advantage of Natures
If you're checking your party now and face-palming at the pitiful selection of Natures, don't fret. Because you can easily conquer the main story with bad Natures. Still, when you're competing against other human trainers or the tougher post-game battles, having a beneficial Nature is one of the first things you need to fix.
In general the best way to decide a Nature is to first identify what your Pokémon excels in, then pick a Nature that helps. For example, if your Pokémon is a physical powerhouse, you'll probably want an Attack-boosting Nature such as Adamant. A Speed-boosting Nature could be useful as well, since Pokémon with higher Speed go first.
In the majority of cases, avoid picking a Nature that doesn't boost any stats, such as Hardy. You may think it's smart to have no weaknesses, but in the dog eat dog world of Pokémon battling, having no strengths is a bad thing. If you want to use both Physical and Special moves, go for a Nature that drops a Defense stat instead.
Likewise, whatever you do, do not bother picking a Nature that covers for a weakness. The boost from a Nature is a 10% multiplier and multiplying a low stat is never as effective as multiplying a high stat. If a Pokémon has a low stat, you'll just have to work around it or use a different Pokémon for the job.
If Pokémon are randomly assigned Natures, how do you even choose them? Do you simply catch a lot of Pokémon and weed through the ones with Natures you don't want? You could, but there are easier ways to get a Nature that you want, although some prior preparation is needed.
A Pokémon with the Synchronize Ability at the front of your party will cause all wild Pokémon to have a 100% chance of having the same Nature as it. Of course, you need to first acquire a Pokémon with Synchronize and the Nature you want. Also, this doesn't work for raids.
When breeding Pokémon, if one of the parents holds the Everstone item, they will pass down their Nature to their offspring 100% of the time. If both parents hold an Everstone, there will be a 50-50 split between which Nature is passed down, so don't do that.
New to Sword and Shield, when you reach the Battle Tower during the post-game, you can earn Mints by ascending the ranks or purchase them using BP. Mints will change the increased and lowered stats resulting from a Pokémon's Nature, effectively overwriting their Nature.
Mints are a game-changer, because they allow you to fix Natures after the fact. But there are two things to be aware of. Firstly, like Bottle Caps, the effect only applies for the Pokémon you used the Mint on--it will not be passed down when breeding.
Secondly, like Bottle Caps, Mints are fairly rare/expensive. As such, you should only use them if necessary--for example, for Legendary or raid Pokémon you've caught. For all other situations, you should aim to get the Nature right the first time!