I'm not sure what you mean by "fail forward,"
The term comes from an approach to action resolution associated especially with Ron Edwards (Sorcerer), Luke Crane (Burning Wheel) and Robin Laws (HeroQuest Revised). As a technique, although without that label, it appears in the 4e DMG and then again, in more detail, in the 4e DMG2 (in the latter book Robin Laws cuts-and-pastes big chunks of the HQ Revised rulebook into the 4e book). The only d20 game I know of to advocated the technique under that name is 13th Age. (Jonathan Tweet is a big fan of the technique. In his preface to the 20th anniversary edition of Over the Edge he says that if he were to write the game now, he would include it as a preferred resolution technique.)
Here is a description (combined with advocacy) of the technique from 13th Age (p 42):
A simple but powerful improvement you can make to your game is to redefine failure as “things go wrong” instead of “the PC isn’t good enough.” Ron Edwards, Luke Crane, and other indie RPG designers have championed this idea, and they’re exactly right. You can call it “fail forward” or “no whiffing.”
The traditional way to interpret a failure is to see it as the character not being up to the task at hand. . .
A more constructive way to interpret failure is as a near-success or event that happens to carry unwanted consequences or side effects. The character probably still fails to achieve the desired goal, but that’s because something happens on the way to the goal rather than because nothing happens.
I personally prefer the description of the technique from Burning Wheel, although I can't give that to you word-for-word here. It is along these lines, though: when a player fails a check don't focus on the idea that the PC failed at the attempted task; rather, emphasise the PC's failure to achieve what they hoped or intended to - which may have happened even if they succeeded at their task (eg because some external element, perhaps one that hitherto hadn't been an established part of the backstory of the game, intervened).
On the same page of 13th Age, there is what I consider a fairly low-pressure example of "fail forward": a failed CHA check to gather information about an NPC's location doesn't mean the information isn't gained, but does mean that the NPC gets word of the PC's inquiries, and hence is prepared and ready (or perhaps has moved on) when the PCs arrive at that location. Burning Wheel tends to emphasise more drastic (and dramatic) sorts of failures: in this case, you learn where the NPC is because you come across them, in the street, trying to find you! But that difference in the degree and immediacy of pressure resulting from the consequences of a failed check is a matter of taste, and not inherent to the technique itself.
Another example I have given on these boards has been in the context of 4e skill challenges: if the low-CHA fighter fails in a Diplomacy check in a skill challenge, you don't have to narrate that as "You cough and splutter all over the NPC". You can instead narrate something like "The NPC nods wisely, and replies - You make a good case, but unfortunately I swore an oath to my late father that I would never take such a course of action, . . " I have mentioned this example because I think it nicely illustrates that "no whiffing" idea - the failure doesn't make the PC look incompetent or idiotic, but is instead used by the GM as an opportunity to introduce an additional complication ("Schroedinger's oath") into the scenario - now, to continue with the skill challenge, the players have to work around the oath or perhaps come up with some idea for relieving the NPC of the burdens of the oath.
It's obvious what happens when you fail the stealth challenge: you get caught
I like the example that [MENTION=20323]Quickleaf[/MENTION] suggested upthread - the players fail their group check to sneak past the bugbears, but the GM narrates the consequence as being that the PCs were not heard by the bugbears: rather, a
prisoner hears them and calls out - so they haven't achieved their goal of getting from A to B stealthily, but their situation isn't framed as being caught either. The situation has become more complicated, but there are still meaningful choices to be made (and hopefully, therefore, fun play to be had).
I hope that these examples also help make clear the sort of playstyle with which fail forward is associated: not so much with Gygaxian-style "skilled play", nor with serious simulation-oriented play (hence [MENTION=2518]Derren[/MENTION] wants it to "die painfully") and more with "keeping the scene alive while there's still fun stuff to be milked from it" play.
I like the angry DM's take on failing forward
The stuff you quote suggests to me that AngryDM doesn't have very much familiarity with the technique. Whether one likes it or not, it has nothing to do with "They just either succeed forward or fail forward until they get to the end." In the sort of play that uses "fail forward" techniques, there
is no "the end". There may be rules for deciding when a scene is to be closed with some final resolution (be that failure or success) or there may not - that depends on system details - but what happens next has to be constructed on the basis of what already happened, including the complications narrated as part of the "fail forward" narration. If you already know what "the end" is - ie if the campaign is prescripted - then fail forward is pointless (and as far as I can see so is any other action resolution, but maybe I'm missing something - perhaps the idea is that to progress through the script the players have to make a certain number of successful checks, and if they don't they go back to the start and try again. That sounds a bit video-gamey to me, though!).
