Straight-forward question. I've seen the terms used a lot, mostly in optimization questions and guides, but they aren't usually explained. From googling, it's easy to find that they are abbreviations for Multiple Ability (score) Dependent and Single Ability (score) Dependent, but I'm not sure what this means. Does MAD mean it isn't viable unless many of their stats get to 20? Is any of them a bad thing? Good thing?
A good answer explains the concepts, if possible its origins, and preferably exemplifies with classes that are clearly MAD or SAD for any specific edition (reason I'm tagging it as D&D, not a specific edition). For clarity, if Ranger was MAD at 3.5e and now it isn't any more, an example using the Ranger from 3.5e is fine. I've seen the term in 3.5, 4 and 5e, as well as Pathfinder, so I don't think the term itself is system-specific, only the examples might be.
It's different from How many Ability Dependencies is too many? (What is MAD?) because that question asks some kind of specific threshold for how many AS dependencies consist in a MAD character in 5e. I'm not interested in something that specific.
Best Answer
MAD
Multiple Ability (score) Dependent means that a class needs high numbers in multiple different ability scores to function well. The archetypal MAD class (in my mind) is the Monk from Pathfinder.
Pathfinder Monks need:
These are of course in addition to Intelligence to get more skill ranks
Right away we see that Monks need 4 (or 5) out of 6 ability scores to be high. Additionally, 3 of those are physical ability scores, and as such share magic item slots for items that enhance them (Str, Dex, and Con are enhanced by belts). Getting 1 or 2 ability scores high isn't too hard, but 4 is.
SAD
Single Ability (score) Dependent means that a class only needs a single ability score to be high to function well. Several classes fall into this category, including most pure casters, ranged fighters, and rogues (depending on archetype).
Pathfinder Wizards need:
There is pretty much nothing a Wizard will want to do that isn't benefited by Int, or that is benefited by other ability scores. They don't even need a high Con since they won't be on the front-line and probably won't be hit.
Because they only need 1 ability score to be high, Wizards can devote more resources into pumping that one score until it is as high as can be, and then direct those resources into other useful items without needing to stretch to cover lots of different scores. Additionally, getting a higher Con is easy since Con boosting items use the Belt slot, while Int boosting items use the Head slot, meaning there is no opportunity cost to increasing both.
What does this all mean?
Basically SAD classes are much easier to make and to play effectively. MAD classes need more resources to achieve similar levels of effectiveness, and may require more real-life time dedicated to finding obscure bonuses and builds to make up for their shortcomings. Additionally MAD classes can find it hard to stay relevant at higher levels as the effective tax on their upgrades takes its toll, especially in a party with SAD classes.
That doesn't mean that SAD classes are inherently better than MAD classes, or that MAD classes can't be effective or fun. Obviously it depends on what system you are playing (Pathfinder is much more punishing than DnD5e, for example), but DnD is a game, and you can have lots of fun with any class. Unless you are playing a high level, optimization heavy, all combat campaign don't feel like you need to shy away from a MAD class, although if you are new to the system it will obviously be easier to go for a SAD class.