Apparently it's a bunch of things... the buzz Immortals feel when another of their kind is near, the energy release that happens when one is beheaded, the ability to feel at one with living things around them (the stag) and the power that makes them immortal itself. Highlander 2 attempts to expand upon this by showing it as a power that "binds" Connor and Ramirez together beyond life and death. There's also a scene in the first movie that makes me think there is some kind of "coming of age" that each Immortal experiences when they are struck by lightning that could be called "the quickening" (unless the scene I'm thinking of is just Ramirez having Connor struck by natural lightning to show him what the real "Quickening" will feel like when he beheads another Immortal, as part of his training).

But as the movies and series progress, it becomes such that "The Quickening" is just an electrical storm when an Immortal gets killed in proximety to another.

Other differences between the US theatrical cut and the Director's cut on DVD (besides those already mentioned), from memory:

The final Quickening is modified. In the original you can barely make out the wires that are lifting Christopher Lambert into the air. In the DC, extra lightning effects were layered over them to cover up the wires, and some extra CG pyrotechnics were added forming a circle around him at various points. The Kurgan's head actually falls off in the original and you see energy underneath it. In the DC his head starts to "crack" from the cut in it and then it pauses as energy surges out of it (like glowing blood or something) and you hear a supernatural "woooO" type sound effect.

The "buzz" of the Immortals is modified. You hear a characteristic humming helicopter (hard to describe) sound effect when Immortals are near each other (for instance in the scene near the beginning where Connor stops suddenly in the parking garage and then steps on a coke can, originally there was no extra sound effect, the "buzz" we hear was inserted, to make it more consistent with the TV series that always plays some sound effect to notify the viewer that Immortals are sensing each other). Originally you had to just go by the acting alone.

The first Quickening is modified. In the DC version, the energy of the quickening that surrounds Fasil's body and levitates it actually forms a "phantom head" (where his head used to be) made out of energy, that wasn't there before.

When Kurgan beheads Ramirez, there's a series of whooshing crackling sound effects that weren't there before. Originally there was just some normal lightning flashes in the background and he's shivering with the unseen power.

But yeah, otherwise it's just spliced in footage from the European/Japanese versions, the removal of the scene of Bedsoe burning himself in his car and the voice over "I want to go home."

What should be preserved is the "making of" featurette that is featured on the recent European "Immortal Edition" set but not the US Immortal Edition (that came out earlier).

Speaking of extras, many pages of publicity still images and script pics from the Laserdisc version were copied over to the 1997 DVD but not the Immortal Edition (due to a glitch, they would speed by the viewer ultra fast, making them impossible to read unless you paused and did frame by frame, rather than the slideshow they were intended to be), also the quality was poor.

The Laserdisc edition supposedly also included a "3D connor macleod sword model" that you could view on the disc, but I never saw what they were talking about.

If somebody wanted to throw those onto a "bonus disc" that would be worth seeing.

Also, I haven't watched the 1997 DVD in years, but some folks claimed, when the Immortal Edition came out, that the new version's audio wasn't quite as good, but I couldn't really tell a difference (I don't have good equipment, I still watch my movies on my computer).