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Normally you'd run binvox on your own PC, where it will use your installed graphics card (unless you are using the “exact voxelization” method).
To run binvox on a headless server instead, either:
install Xvfb (on CentOS, for example:
yum install xorg-x11-server-Xvfb ),
then start a virtual screen: After this you can run binvox.
Note: with newer versions of Xvfb and/or Mesa (I still have to figure out where the problem lies) it no longer seems to be possible to use “pbuffers” on a virtual screen, so you won't be able to use the -pb option. (also see this bug report). In this case, it may be that the Xvfb screen has to be large enough to support the size you're voxelizing at, please let me know your experiences with this.
(thanks to @vineet7kumar for figuring this out)