The Universal Morphing Grid is an energy field which gives the Power to any Ranger. It was first mentioned by Zordon. It was assumed and then proven in "Once A Ranger" that it gives the Power to every generation of Power Rangers. And each team of Rangers has a specific link to the Morphing Grid. When a Ranger morphs, they use their morphers to create an entryway, and pass through the Morphing Grid to gain their powers.
The grid's physical form was only shown once in the Power Rangers Dino Thunder wrap-up special leading up to Power Rangers SPD. The grid's physical form is a large boulder with a large gem on top. This form functions like an absorbing device allowing Rangers to add their Ranger memories to the Morphing Grid. In this form it also functions like a crystal ball, allowing Rangers a small glimpse of future Rangers and their battles. Once a Ranger's memories have been added to the grid, it will go to a stand-by mode so only future Rangers can insert their memories.
In Season 2 of MMPR, it was mentioned by Lord Zedd that the Grid is maintained by a balance between the major forces of Good and the major forces of Evil, i.e. in that time period, Zordon and Lord Zedd.
In Dino Thunder, it was revealed that Tommy Oliver found the Grid's physical form and used it to create the Ranger Archives with information of every generation of Power Rangers leading up to that point in time. It was also seen that when two rangers of the same color and power exist, one of them will have to go. This case was shown between Trent and the White Ranger Clone. This was also mentioned back in "Wild West Rangers" when Zordon forbade the use of the second Pink Pterodactyl Coin stating "Too much pink energy is Dangerous."
In the Operation Overdrive team-up "Once A Ranger", the Morphing Grid was damaged by the combined powers of Thrax, Flurious, Moltor, Miratrix, Kamdor, Mig, and Benglo. The grid was shown to have massive electric surges firing off inside. When the Sentinel Knight restored the Veteran Rangers' powers, it was shown that the only part of the grid that had been damaged was the section that connected to the Overdrive Rangers. Andrew Hartford managed to reinforce the Grid to prevent further damage, but it had to be repaired from the inside, which Alpha 6 did.
Much of the grid is unknown or not explained in the series. Zordon has mentioned twice that the destruction of the Rangers's Zords would destroy their powers (it is unknown if this is true with other Ranger teams after Mighty Morphin) as happened with the Thunderzords. However, many Rangers have had their Zords destroyed in combat (usually by self-destruction), yet have kept their powers soon after.
When Lord Zedd first attempted to destroy the Zords in "The Mutiny" the Rangers did not lose their powers due to the lost Dinozords because Alpha 5 rescued what he could to create the Thunderzords (it is assumed that what remained of the original Dinozords was used to create new Dinozords since they are components of the Thunderzords).
It should also be noted that Alpha 6 tells Adam Park in his appearance on "In Space" that his use of a damaged Morpher (also mentions the Power Coins were destroyed but it is assumed only the power, not the coins themselves since Adam still had his) might kill him and during the episode Adam starts to lose his powers after he morphs which takes a physical toll on his body.
In RPM, Dr. K explains that she discovered a "Bio Field" of energy from which she was able to draw power for the RPM Rangers and their subsequent weapons. Though it is never identified as such in the series, it is implied and assumed by many fans that what she calls the "Bio Field" is meant to be the Morphing Grid.