Online level sharing is a planned feature. From within the game, you'll be able to browse levels that other players have created, download and play them, and upload your own levels to share with others. In the meantime, here's where your levels are saved:
Linux/Mac: ~/.local/share/godot/app_userdata/Gravity/levels Windows: C:\Users\USER\AppData\Roaming\Godot\app_userdata\Gravity\levels
Levels are stored in plain text so they are small and easy to share. You can make a copy and send it to anyone by email, Dropbox, Discord, etc. Then they'll need to save the level on their computer, open the editor, load it, and play it.