I pulled this out of another response and tidied it up as it captures something I've been mulling. Maybe 5e ability checks are helpfully explained like this, using the example of opening a safe
- It may seem counter-intuitive, but in 5e, you don't really roll to open a safe
- Per DMG 237, what you are really rolling for are consequences
- Taken together with PHB 174, the results can be
- you open the safe (the consequence you want)
- you open the safe but with additional consequences
- you become engaged with some consequences
For emphasis, per RAW, outcomes of ability checks in 5e - pass or fail - are ordinarily not inert. I'm not saying a dead-end
couldn't ever come up in an interesting way, but that isn't the default.
I can wonder - what if the safe is empty? The answer depends on decisions about the kind of play I am interested in. Perhaps an immersionist would like to imagine possibly empty safes.
I can wonder - what consequences? For me, the answer is constrained by fiction, description, and system. For another DM, the answer could be entirely different. And that will matter. For 5e, system
and DM matters. Because consequences are what justified calling for a check, they're known
going in. Thus one could most accurately characterise 5e ability checks as
consequence-resolution.
In understanding ability checks for 5e, folk normally start with examples like the one in the primer. Later, they might read the
PHB 174 and see they should take uncertainty into account and can narrate complications on failure. Eventually, they'll get familiar with
DMG 237 and see what's possible: that 5e uses what I'm calling consequence-resolution. Stopping short at primer or PHB leaves the picture incomplete. Because in D&D
system + DM matters, even the whole picture won't guarantee that any two groups will play it the same way.
[EDITED To tighten up a few elements.]