IIIF, pronounced "triple-eye-eff", is a set of standards for working with digital objects on the web, such as digitised books, manuscripts, artworks, movies and audio. It's typically used by galleries, libraries, archives and museums to present their collections and make them interoperable - they become available to software such as viewers, annotation tools, digital exhibits and more. Learn more at iiif.io.
A Manifest is the The unit of distribution of IIIF. It's like a web page, but instead of HTML for browsers, it contains JSON data for IIIF-compatible viewers and other software. A IIIF Viewer loads a Manifest and generates the UI to allow the user to navigate around, e.g., from page to page of a book, or from scene to scene of an opera. This Manifest Editor allows you to create new Manifests - from scratch, or by adapting existing ones.
A Canvas is a bit like a PowerPoint slide - the virtual space that content is arranged on. A Manifest has one or more of these "slides" - for example, one for each page of a book - and each slide has content - most commonly, one image filling the whole Canvas. Rather than a Manifest having a simple list of images, it has a sequence of Canvases, and each Canvas has one (or sometimes more) images (or AV content).