A battle format (or just 'format') is a pre-existing set of rules that you can use in competitive play. It decides which Pokemon are allowed, whether the battles are singles or doubles (or something else), what items are banned, and many other things.
There are many battle formats – which one to use is decided before the battle, e.g. when you queue for a match. Some formats are "official" (i.e. they can be selected in-game), while others are run by a competitive battling community called Smogon and played on Showdown.
Battle formats have names to help you tell them apart. Here is a list of formats for Gen 8. Below are some examples of battle formats you may already be familiar with:
- Battle Stadium Singles (BSS), which is the format you play when you queue ranked single battles on your Sword/Shield game. BSS has different "series", listed here.
- VGC (or Battle Stadium Doubles), which is the tournament-standard doubles format used in official competitions. VGC also has different series.
- OU, which is the playable singles battle format based around the Smogon tier, OU. You can read more about tiers here.
- There are some other formats which are not listed on Smogon, e.g. "Casual Battles" in the Battle Stadium on Sword/Shield, which is a 3v3 singles format that allows legendaries.
Each battle format has different rules. This means different Pokemon and strategies are most effective in each format. The state of strategy in a format can be called the "metagame" or "meta". Building teams and strategies around the meta is one of the pivotal aspects of competitive Pokemon.
The rules of battle formats change frequently, especially when a new generation is released and new Pokemon cause the metagame to shift. Because of this, it's useful to mention the generation as well as the format when sharing strategies or asking for advice.
To choose a format to play, pick a Pokemon you like and research where it is viable. For example, if I like Gyarados, then I might play Gen 8 UU because Gyarados is very strong in that format.