The Series Is are based on the Colt Series 70 style with no firing pin safety.
The Series IIs are based on the Colt Series 80 style with the firing pin safety.
In the slide of the Series II there is a small "button" (the firing pin block) that is disengaged by a small pin in the frame (the firing pin block lifter) located beside the disconnector that is pressed up when you engage the grip safety. The pin pushes up the firing pin block on the bottom of the slide which, in essence, releases your firing pin and allows it to fire.
Most 1911 fans don't like the Series 80/Series II safeties as it is one more thing that can break, and requires the gun to be disassembled a little differently. Also, some guns with the series 80/series II safeties are a little more fussy in operation. In some guns the pin may be too short and not push up on the "button" as well as it should. Mainly this is due to incorrect take down and reassembly.
The difference in field stripping is that the grip safety MUST NOT be pressed in during take down and reassembly or the slide will damage the pin that lifts the "button." The pin sticks up out of the frame when the grips safety is pushed in. If done incorrectly you can damage the pin and the safety won't work.
Pics:
Series I Slide (no firing pin block):
Series I Frame (no firing pin block lifter):
Series II Slide (with firing pin block):
Series II Frame (with firing pin block lifter beside the disconnector):