Pause Buffering is a technique used to do specific inputs on exact frames. It is often very helpful to use it to perfectly time precise tricks.
While you unpause the game, there is some lag that happens between the pause menu disappearing and the game moving again. During this time, your inputs are not tracked by the game, so holding buttons during this period of time will execute the input on the first possible frame after the unpause.
For example, try running forward and pausing the game. Continue holding up, and start holding A. Unpause the game. Link will just continue running forward and not roll. The input was tracked during the pause menu, so it counted as holding the button instead of a new press when you unpaused.
Now try the same thing, except don't hold A until the unpause lag happens. This time, Link will roll on the first frame the game is unpaused. The game never tracked the A button as being held, so it sees the input happening on the first frame the game resumes play.
This is more relevant for button presses that wouldn't be executed by holding the button down. Shielding or moving the control stick are a continuous input so they do not need to be buffered.
For some reason, you cannot pause buffer speaking to an NPC. Instead, a roll will come out. One use of this is to pause after buying the shield, equipping it, and then rolling out of the shop to save a very small amount of time (rolling would normally be impossible in this situation because Attack will not appear on your A button).
In order to advance frames, you still must time exact pauses. Buffering a pause input will actually pause on the same frame the game was already paused on. This is the most difficult part of pause buffering.
Pause buffering is slightly different on the different console versions of the game, this is due to the amount of unpause-lag. Pause buffering is least laggy on VC thus the most direct, and hardest on N64 which has the most unpause-lag. With practice however, pause buffering consistently shouldn't be a problem on whatever your console of choice may be.