A Hydrogen Bond Network is a 'web' of hydrogen bonds that connects the sidechains of multiple residues. When constructed across protein interfaces, these networks help to make the interface more stable.
Hydrogen Bond Network Filter
Introduced in May 2015 this filter allows folders to improve the stability of their folds.
bkoep's clarification from the blog comments:
In Foldit, all CPK modes (including Score/Hydro+CPK) color nitrogen atoms blue and oxygen atoms red. Imagining blue donors and red acceptors is a helpful simplification, but is not strictly correct. While nitrogen is usually a donor and oxygen is usually an acceptor, there are exceptions to this rule. For example, the <a href="http://www.cryst.bbk.ac.uk/PPS2/course/section7/os_hres.gif">link above</a> shows that one N of histidine can accept an H-bond, whereas the O of serine can also donate an H-bond.
This link in particular should be helpful for determining how many hydrogen bonds are required to completely satisfy each residue type. For example, note that the N of tryptophan can only make one H-bond, whereas the N of lysine can make three!