In terms of a trunk radio system, "affiliation" means that a radio has been turned on to a specific talkgroup (or site). Trunk systems track what their radios are doing at all times, so if you are running a trunk exploring program like Unitrunker (or, are a professional system admin using something like Motorola's ZoneWatch/SystemWatch), you can watch radios 'affiliate' and 'deaffiliate' from sites and talkgroups all day long.
No scanner will show you which radios are on the TG you're monitoring; the display would never stop blinking radio IDs on some bigger systems. IIRC, only the GREs show the radio IDs that actually transmit on given talkgroups (something I hope will be rectified early on in the new 396XT's upgrade cycle).
It's sometimes amusing to watch radio affils if you are playing with a program like Unitrunker. For example, on my local public safety system, radio 1234 talking to radio 5678 might say "Come over to channel A4 with me for a second so I can tell you about this patient" ... and all of a sudden, 40+ radios affiliate (sign on) to talkgroup A4 ... :lol: