Microsoft Edge browser for Android is not publicly available on Google Play Store. The app is still in its development stage and its possible to have a few glitches here and there yet you can go ahead and install it.
Last week Microsoft released Edge on iOS and Android for Windows Insider users exclusively. The iOS version was limited to 10000 Apple users for a TestFlight app which was exceeded and is currently not available to anyone.
The Edge browsers on iOS and Android is basically for users who have Edge browser on desktop and wish to sync their bookmarks, history, passwords and more on their mobile browser. The Edge browser is similar to Safari/ Chrome browser underneath on mobile, however, from the outside it features a familiar for Edge users. It also comes with features like Hub View, Reading View, QR-code reader, voice search and more.