There are numerous FAA requirements about this depending on if you are IFR/VFR, the airport, the expected weather, etc. but the bottom line is sufficient fuel to:
1) Fly to your intended destination.
2) Fly from the destination to the alternate (if required).
3) Fly for an additional 45 minutes at normal cruise speed (minimum).
What the pilot was saying was that they had 20 more minutes until they had to go to Pittsburgh. If it took 45 minutes instead of 20, it was because the computer calculated that was exactly how much more time they could hold.
There was no gliding on your flight. It may have felt that way during a descent at flight idle.
The flight may have been scary to the passengers, and people may not have wanted to get back on, but I'm sure it was quite routine to the people up front.
Source: US certified commercial pilot, Aero. Sci. degree. Certified ATC.