Branded Keyword is a search term containing a brand or app name — either your own (protecting it) or a competitor's (bidding or ranking against it).
Branded keywords split into two strategies. Defending your own brand means making sure you rank first when users search your name — usually automatic for an established app, but worth confirming, since competitors can rank or run Apple Search Ads against your brand term and skim your highest-intent traffic. Targeting a competitor's brand means trying to appear when users search for them; organic ranking on a rival's name is hard, so this is mostly an Apple Search Ads play.
Branded traffic is the highest-intent traffic there is — the user already wants a specific app — which is why both protecting and contesting brand terms matters. Apple's guidelines restrict putting competitor brand names in your metadata, so competitor-brand targeting lives almost entirely in paid search, not organic ASO.
Example
A challenger budgeting app runs an Apple Search Ads campaign on the competitor term "Mint" to capture users actively shopping for a money app, while making sure it ranks #1 on its own brand name organically. Confirm you rank first on your own name too — competitors can run paid search against your brand and skim its high-intent traffic.