AD&D 2nd edition is basically AD&D with Non-weapon proficiencies. D&D was the first role-playing game, followed closely by AD&D. These systems were class-based, meaning that the abilities your character had were class specific: the thief had Move Silently for example, and no other class had that ability (to some extend).
After AD&D, many other systems came out, notably RuneQuest, where there were no classes. Your character had an occupation that gave you a bundle of skills to start with, but you could learn any skill you wanted. It was a skill-based game, as opposed to the class-based system of AD&D. Skills openend a whole new level of play, and TSR’s answer to that RPG development was to release AD&D 2nd edition which included Non-weapon proficiencies (NWP), a kind of skill system.
The problem is that it was a add-on and it didn’t really fit very well with the system. For one thing, NWPs were based on characteristics, for instance Rope Use was based on Dexterity, and Reading Lips was based on Intelligence -2. That’s all fine when you’re first level, but the thing is that your characteristics don’t improve over time, so your NWPs were set in stone. Yes, you gained a few NWP “slots” over time, but not very fast and more often than not you chose a new NWP instead of improving one that you already had. So these were “static skills”, and one thing that is fun about RPGs is the sense that your character is improving.
But there were also many other ‘improvements’ in this second edition. The foremost was that the rules were more logically laid out (a big complain about the first edition). It also used THAC0S, something that most of us had worked out in first edition, instead of attack tables per class. It also simplified the AC adjustements for weapons to 3 numbers instead of the full 19 numbers table (that just about noone used). So overall it made a number of improvements, most of which felt like updating the rules to what most people were house-ruling anyways. But it made the system easier to get into for newcomers (and those with the feeling that you can’t change the rules to fit your taste).