The Pocket Dimension is a dimension referred to by Professor Quadwrangle. Following the catastrophe at the game's beginning, the Professor becomes trapped in this dimension and requires the player's help to find out how he got there and eventually allow him to escape.
Though it is never shown, the Professor describes the dimension as full of items that would typically be found in one's pockets such as cell phones, keys, candies, and gum.
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Plot details follow.
Upon restoring power to the Uber-IDS the Professor finally remembers that the Pocket Dimension was meant to serve as a fail-safe should anything go wrong and that he was transported there on purpose to protect himself. His memory restored, the Professor also remembers that the generators the player has spent the game restarting should have been left alone. With power restored, the IDS device now once again threatens the destruction of Quadwrangle Manor.
Quadwrangle instructs the player to get to the center of the Uber-IDS, trapping but protecting the player character in the Pocket Dimension while finally freeing the Professor.
His nephew safe for the moment, the Professor states that it is now up to him to deal with the aftermath. The game ends by implying that the Uber-IDS is inadvertently causing dimensional shifts over a much larger area, possibly the entire planet.