Feature flags are just checks that let you enable or disable code paths at runtime. For example, say you're rewriting the profile page for your app. Instead of just replacing the old code with the new code, you'd do something like:

if (featureIsEnabled('profile_v2')) {
  // new code
} else {
  // old code
}

Then you'd have some UI to enable or disable the flag. If anything goes wrong with the new page after launch, flip the flag and it'll switch back to the old version without having to modify the code or redeploy the site.

Fancier gating systems let you do things like roll out to a subset of users (eg a percentage of all users, or to 50% of a particular country, 20% of people that use the site in English, etc) and also let you create a control group in order to compare metrics between users in the test group and users in the control group.

Larger companies all have custom in-house systems for this, but I'm sure there's some libraries that make it easy too.

At my workplace, we don't have any Git feature branches. Instead, all changes are merged directly to trunk/master, and new features are all gated using feature flags.