nothing special. u just "flash" your aircraft radar data block at the next guy down the line. when they see the flash and accept the aircraft by suppressing the flash, then you can have the pilot change to the next guys frequency and they will now be responsible for you.
there's many reasons the guys was waiting for the next controller to accept the handoff.
-maybe the next guy had the range on his radar dialed way in so he just physically was unable to see your target on his scope yet.
-too busy to accept the next airplane
-too slow to accept the next airplane (talking to neighbor)
-previous guy started flashing your aircraft 100 miles too early, next guy just doesn't want to be responsible for you that far away from his airspace
-those two controllers pissed at each other for something
the list could go on and on...usually it cuz the next guy is too busy at the moment though.