The details of how warp drive operated were not fully realized by the time Star Trek: The Next Generation went into production. It was Rick Sternbach who decided that main engineering was where the matter/antimatter reaction needed for faster-than-light space travel would form.
The vertical warp core had already been introduced in Star Trek: The Motion Picture. The thinking at the time was that the antimatter would be in a magnetic containment at the bottom of the engineering hull, sending antimatter up into the reaction chamber.
The shaft above engineering, however, did not make sense. There was no place where the “matter” was coming from.
Sternbach solved that problem by placing deuterium tanks at the top of the Enterprise-D’s warp core, which provided the necessary matter.
“When the time came to do TNG, Mike Okuda and I sat down over many pizzas and bowls of noodles to compile and clarify all of the information we had on impulse, warp, power generation and so on,” he told Forgotten Trek in 2007.
The Original Series touched on many of these concepts but wasn’t clear or consistent, so we wrote a lot of memos which eventually became the TNG Technical Manual.
The engineering set was a redress of The Motion Picture‘s, erected on Paramount’s Stage 9. The round reaction chamber, containing the dilithium crystals, was based on the warp core that had been built for the aborted second Star Trek television series, Phase II, which had been designed by Mike Minor. It was redressed again to become the engine room of the Enterprise-E in First Contact.
The structural elements of the second floor were kept intact while the rest of the set was rebuilt. It was given an open floor plan, with several corridors providing access to the room.
Light fixtures were added to either side of the master systems display midway through the first season and the display itself was updated (the color scheme changed from green to blue) in season 3.
The “pool table” was introduced in “No Where No One Has Gone Before”. Early in the episode, the main corridor passing through the set was still half-open. Later in the episode, the same doorframe is walled off with a console. It would be permanently blocked from the second season onward.
The entire area was frequently redressed as a large corridor junction to allow for longer walking scenes.