In the late 80's/early 90's, I worked on a ramp a Toronto Intl (YYZ), for a Corporate Jet FBO (Fixed Base Operator). Our customer pilots that were scheduled to depart at a certain time on a specific day needed to contact ATC's flight services and arrange for a departure "Block Time". I could do this on behalf of the pilots if they requested it. This was a "one hour" period of time in which their aircraft was allowed to depart. I believe the purpose of this procedure was to give ATC an idea of how many aircraft to expect for departure at that time of day. I think the rule was that a pilot had to start taxiing within one hour after his given Block Time (a 1 hour grace period). So, if your given Block Time was 10:00 am, you had up to 11:00 am to contact Ground Control for taxi clearance.
Only a certain amount of Block Time hours were availiable for each hour of the day (a way for ATC to control the amount of aircraft movements), so if a pilot forgot to arrange for a "Block Time" for the hour he was scheduled to depart, well, he'd have to wait for the next availiable one. Also, if a pilot didn't contact ATC within this one hour period of time, not only would he NOT be given a clearance, he could be fined money for the inconvienance he caused the Block Time system (because another aircraft wanting to depart could have used that time).
You could cancel your Block Time if something was causing a delay, such a passengers, maintenance, weather, etc, however, ATC wouldn't appreciate this being done at the last minute.
I hope this is the same type of "Block Time" you are asking about. It aplies to all aircraft movements at an airport that uses this system (GA, corporate and commercial aircraft).
I suspect that if Block Times were/are used for departures, then they could apply to arrivals as well. Although arrival Block Times might have different rules.
PS, guys, if my memory of a "Block Time" is way off the mark....please set me straight!