It gives a bare-bones environment for you to run your programs that is presumably very low overhead. Think of it as an embedded system where programs run without an OS. This is the environment a program running inside zerovm will see. All you have is libc and the zerovm-provided APIs. If you want more, you'll have to statically link your programs.
The thing is, you can run many, lets say thousands, of these little programs inside a single machine in such a way that each one can never see the other ones (as long as it's impossible to break out of the ZeroVM sandbox).
Such a technology would enable neat stuff, like renting a server for someone to run a single program for some period of time and have the results sent back. Nobody does this for unrestricted programs today, for many reasons, a very important one being the fact that it would be very hard to do this in a secure way.
The "run a C program for some period of time thing" would work kind of like the AWS dashboard, but instead of having to spin up a machine with linux on it and running your program inside that, you would only upload your binary and a manifest file. Kind of like what app engine does, but with less restrictions (you'll probably be able to do anything as long as you're able to compile a "safe" binary that does it).