Mergi checks xssit.com for new versions and installs them for you, from inside the app.

When Mergi checks

With Check for updates automatically on (Settings › Updates), a short while after it starts and then about every six hours.
Whenever you click Check now in Settings, or Check for updates in the tray menu.

When a new version is out

A note at the bottom of the window says so, and a download badge shows in the title bar while it waits.
See what is new opens the offer with the release notes, and three choices: Install now, Later or Skip this version (Mergi will not offer that version again).
Install now downloads the update and checks it, closes Mergi, installs it and opens Mergi again. Your settings, files and licence stay.
After the update, the What's new window shows what changed.

A required update cannot be skipped: that version of Mergi can no longer be used, and Mergi asks you to install the new one to go on.

Only the installed Mergi can update itself. A copy that was not installed with the setup program shows the link to the website instead.
The update is downloaded from xssit.com and checked before anything is installed.