What is /Users/me/Applications?

Anything can create ~/Applications.

It's usually used to store apps that you don't want to (or can't because you're not admin) install globally on the system. The folder doesn't exist by default, but if created it will be given a custom icon like /Applications. Any app on the system can create this folder and since no record of what app created it exists you probably won't know.

/Users/<username>/Applications or ~/Applications is your user's Applications folder. Much like your Desktop, Documents, et al., this folder is local to the user and can be changed by (natively) only that same user. Very nice if you want to install an application for only yourself and no one else.

/Applications is your system-level Applications folder, visible and accessible by all users on the system. To make changes on the system-level, you must authenticate as an admin.

grgarside is right: the folder isn't there by default. You can add it yourself or an installer (e.g. Spotify's installer) can create it for you.