It just meant that this new class had new abililties BEYOND what we already played with. Thus...the thief could try to move absolutely silently...but if they failed...well...they could still try to move quietly. They basically got double rolls.
OR...another way of doing it was that the Thief would accomplish these things automatically unless they were challenged...or had to do it under pressure...
OR...another way of doing it was that not only would the Thief accomplish normal things automatically (such as moving quietly), they could also try for the supernatural idea of hiding in the Monster's shadow when it wasn't looking...etc.
Unfortunately, the AD&D rulebooks were not that clear on this...and then we got an entire generation that thought differently and hence was born the idea that no one could play hide and seek anymore...or if they did they only could do it by rolling on the lowest tier of the thief ability tables.
OD&D was not clear on this either, it pretty much said they could hide and left it at that. Hear noise used the same mechanic that everyone already could (humans hear noises through a door on 1 out of 1d6, and nonhumans on 1-2 of 1d6) but with better chances (1-2 of a 1d6 at 1st level and improving at higher levels). I would not expect double rolls.
I felt the AD&D books were pretty clear the other way, that hide in shadows was not the ability to mystically step into a monster's shadow to hide but mundane hiding. The move silent ability is explicitly not even silent.
"Moving silently is the ability to move
with little sound and disturbance, even across a squeaky wooden floor, for instance. It is an ability which improves with experience."
"Hiding in shadows is the ability to blend into dark areas, to flatten oneself, and by remaining motionless when in sight, to remain unobserved.
It is a function of dress and practice."
"Hiding in Shadows cannot be accomplished under direct observation. It can be accomplished with respect to creatures with infravision (q.v.) only if some heat producing light source is near to the creature or to the thief attempting to so hide."
"Hide In Shadows: As is plainly stated in PLAYERS HANDBOOK, this is NEVER possible under direct (or even indirect) observation. If the thief insists on trying, allow the attempt and throw dice, but don’t bother to read them, as the fool is as obvious as a coal pile in a ballroom. Likewise, if a hidden thief attempts movement while under observation, the proverbial jig is up for him or her. Naturally, a creature closely pressed in melee is not likely to bother with looking for some thief not directly in the line of sight, but if vision would normally extend to the thief’s area of activity, then observation rules apply. Unobserved attempts to hide in shadows must likewise stand the hazard of the dice roll. A score greater than the required number shows that the character’s ability is not on a par with his or her intent, and although he or she THINKS hiding has been successful, the creature looking in that direction will note a suspicious outline, form, or whatever. Note also that a thief hiding in shadows is still subject to detection just as if he or she was invisible (see INVISIBILITY, DETECTION OF INVISIBILITY table"