Retaining wall movement can be due to a variety of reasons. The most common is a failure to provide an escape route for ground water that may collect behind it. Here in the Northeast, with the normal freeze/thaw cycles of winter, knowing that water expands as it freezes, that can mean substantial movement as the years pass and water pressure behind the wall isn't taken care of. Usually that happens when the wall creates an impermeable barrier...like concrete or mortared stone without free draining gravel backfill and weeps or drain pipe behind it. It can still happen with dry set stone, but that pretty much will only happen when the backfill is a loamy clayey soil through which water can't flow easily. Other reasons can be a change in the load above the wall, or just plain failure of the material with which the wall was constructed. Chances are that your wall moved because of the former...water not being able to drain though it...but that's only a guess, as internet diagnosises are subject to being.

In any case, it sounds like you're faced with dismantling the wall, removing any impermeable backfill within a foot of the back of the wall, and then reconstructing the wall with an appropriate batter (tilt towards the back - not a lot, only about a half to an inch of tilt per foot of wall height), and backfilling with clean gravel. If the stone is to be mortared in place, you'll need to install weeps about every 8 to 10 feet about 6 inches up from the bottom of the wall on the low side. Weeps are really just pieces of small diameter pipe (1-2 inches) with screening covering the buried end that project through the wall (front to back) allowing any groundwater that collects there to drain away. If the wall is to be dryset, some folks might still recommend the weeps, but the spaces between the stones should provide ample area through which the water can flow.