How does herpes (HSV) infection suppress HIV?
Alright, having read the citation linked, and doing a little poking of my own, here's my approach at an answer:

Some human herpes virus infections may compete with HIV infection. Essentially, some strains (not the ones you normally think of) infect CD4 cells - the same cells targeted by HIV. These strains down regulate transcription in CD4 cells, which in turn interferes with the HIV infection process. This pertains, it appears most notably, to HHV-7.

However the actual impact on HIV disease isn't clear. Strain competition triggers some fascinating evolutionary pressures, but HIV is notoriously prone to mutation, and competition for CD4 cells might not impact HIV infection on a clinical - rather than microbiological - scale.

Additionally, the two most commonly thought of forms of herpesvirus infection, HSV-1 and HSV-2 are associated with increased acquisition of HIV infection. The clearest reasons for this are genital lesions and inflammation at the site of HIV infection. There's also some interesting dynamics in play for active coinfection, such as the impact of acyclovir treatment for HSV impacting HIV, or HAART treatment for HIV impacting HSV.