My understanding is that latent HIV reservoirs are a group of immune system cells (CD4+ T-Cells) in the body that are infected with HIV but are not actively producing new HIV. When these cells aren’t actively producing the virus they are basically invisible or unnoticeable by the heathy immune system. They have been known to stay inactive for 10years.
These cells generally reside in secondary lymph nodes, the spleen and the gut mucosa, the vast majority of the virus resides in these tissues.