Assuming that the airfield has an ATIS, "Information Foxtrot" would mean that the inbound aircraft has listened to the broadcast information (weather, rwy in use etc) given on the airfield ATIS freq., and therefore is current with the latest arrival information, which is given a phonetic alphabet letter to identify it as part of the broadcast.
"with Information Foxtrot" means that the aircraft listened to the ATIS, and the information it recieved is called "information foxtrot". Since the information changes throughout the day, every time the ATIS broadcast changes, it is given a new letter.
It's basically a quick way of passing arrival information for an airfield, and saves ATC having to repeat a lot of information on the one frequency every time a new aircraft contacts the field.
Hope this helps.