It is still kind of hard to get a sense of what this project is. To be honest, I didn't even fully get it until I'd managed to get it installed and play with it a little. This is my understanding of the project, someone who is more closely involved can probably correct any errors I might be making here.
MediaGoblin is a backend system for hosting "media". Part of the big idea is that "media" potentially includes any kind of thing you want to host. It's first incarnation was really just for photos/still images (like piwigo or gallery), but now also handles video, audio, "raw" images, PDF, .stl 3d models, Ascii Art, and apparently blog-style HTML text. I'm not sure if it's planned, but I'd expect it to also end up with support for .svg graphics, additional document formats (.odf, etc) and various others as interest develops. I, personally, would love to see .epub support.
MediaGoblin's main purpose is to take uploaded media and catalog it, tag it, generate "thumbnail"images, and perform any additional processing needed (such as producing legally-free format media for streaming and/or download - this IS a GNU-affiliated project after all.) It also handles authentication, access control, generation of the HTML for the pages that present the media, and so on. It is NOT (really) the frontend - they assume you have your own webserver. (There is a minimal python web-server script included can be used but it's not really intended for more than basic testing.
There is currently a focus on developing federation, meaning people can run their own individual hosts with their own login accounts, but be able to use and share media between different hosts without needing separate accounts on all of them. This will make it easy to spread out the hosting and mirroring of media across different servers in different places, which will be useful for load-spreading (like bittorrent) and for "censorship-resistance". (For a large organization with a worldwide spread of MediaGoblin instances, it could be like a Streisand-effect amplifier...)
The buzzword version of the description goes something like this: it's a unified (because this one system handles more or less all types of "content"), decentralized (because multiple independent servers can allow data-sharing and authentication with each other to prevent loss of one server from stopping access to media), federated (that's the buzzword for "one server can be told to trust another server's authentication" thing) system for hosting any "content" (or "media" if you prefer) that you want.
The short version is that it does the same sort of thing as flickr(/piwigo/gallery/picasa...), youtube(/vimeo, etc), soundcloud(/jamendo etc), wordpress, and various others, but it does it all in one interface in a way that the owners have control over so that (for example) some buttnugget can't shut off your video by just telling Google that the sound of birds in the background of your video is pirated music.
It'll currently mostly be of interest to people who are capable of operating their own servers rather than "end-users", though it seems obvious that the expectation is that people will end up using this system to set up hosting for said "end-users", whether for the general public or for use by members of some organization or other. I could imagine a university using it for inter-departmental or inter-campus media sharing and hosting, or an activist organization setting up federated instances in several countries for storing and sharing media, or a commercial start-up basing a multi-media Jamendo-style hosting company on the platform, for example.
My personal opinion: in its current state it's still too difficult install to be worthwhile for, say, a photo-gallery site (piwigo was a much simpler install on my existing webserver), but I don't know of anything similar for hosting video, audio, etc. (I suspect some projects for each on exist, I just don't know of them), and if I wanted to host several of these media types it might be worth it. My main complaints right now are that audio support is limited to offering "webm [v1] audio" (Vorbis audio in a limited Matroska container) as the output format (it can accept any kind of audio as input that gstreamer can handle i.e. just about anything), which is pretty well supported in browsers but not really widely used for audio files. (I'd like to see at least.opus support. .flac and .ogg [vorbis] output as well would be ideal. WebM v2 [opus audio in the aforementioned limited Matroska container] will probably also be handy if Google maintains their commitment to the format, and maybe alac ".m4a" as the only legally-free(?) media format Apple allows people to use as far as I know, besides possibly ".wav"), and that installation is currently quite laborious, especially if you don't want to set up a dedicated server just for MediaGoblin (i.e. if you already have a webserver hosting other things that you also want to serve MediaGoblin-hosted data through at the same time), but what I saw of the last version I tried out it looked promising. I'll be trying it again once I think I can get it to serve .opus audio.