WebExtensions are a cross-browser system for developing browser add-ons. To a large extent the API is compatible with the extension API supported by Google Chrome and Opera. Extensions written for these browsers will in most cases run in Firefox or Microsoft Edge with just a few changes. The API is also fully compatible with multiprocess Firefox.
We're also intending to extend the APIs to support the needs of add-on developers, so if you have ideas, we'd love to hear them. You can reach us on the dev-addons mailing list or #webextensions on IRC.
Before WebExtensions, you could develop Firefox add-ons using one of three different systems: XUL/XPCOM overlays, bootstrapped extensions, or the Add-on SDK. In the future, WebExtensions will be the recommended way to develop Firefox add-ons, and other systems will be deprecated.