To know the context could be helpful.
Usually it means something like "the very", "the particular" or "the precise"
то самое место где я родился — the very place where I was born.
Edit: in this case it most likely means just "that" or rather something you don't necessarily want to name, because it probably has to do with a sexual or politically incorrect subject or there are too many people around who shouldn't actually be hearing your private talk. It is a highly uncommon expression however, I don't believe I have ever heard it. The more common one is "это". In the late 1990s there was a talk show on the Russian TV called "Про это" ("About That") moderated by Елена Ханга, where they talked about sexual matters. It probably could also have been called "Про то самое".