MOOSE directly relies on the libMesh finite-element framework. Because of this strong tie MOOSE contains a particular version of libMesh that we have vetted for our users. To pull down and compile this version of libMesh you simply need to run a script in MOOSE:
cd ~/projects/moose ./scripts/update_and_rebuild_libmesh.sh
Do not use
sudo when running update_and_rebuild_libmesh.sh.