What is the ~/Applications directory for?

An Applications directory in your user's home directory is not a standard directory, but some users create and use them. If you have it, either you, someone else, or some script created it.

In older versions of macOS, it usually does not matter much where you store your app; they are location independent. It often even happened (and still happens) that users downloaded disk images (.dmg) and ran the contained applications from that image, not being aware that the app is not stored in a "normal" volume. So instead of copying an app to /Applications (which requires administrator privileges and makes the app available to all users on the system), some users prefer or preferred to store their apps in a folder in their home directory. A natural choice for that is to create an Applications folder.

Nowadays, some OS restrictions may require you to store the app in /Applications. App Store managed apps live there, and apps that have a System Extension must also be stored there (or else the System Extension cannot get activated; the reasons for that are a bit complicated and relate to the OS' need to manage the System Extensions and keep track of their "parent" apps).