"The Three Pillars" are something of an opaque buzzphrase surrounding a lot of 5e development. Here's how to make sense of it.
What Do Characters Do?
The realization of "three pillars" comes from one basic question: What is it that D&D characters actually do?
To help with this empirically, we look at what D&D players have needed rules for over the course of 30+ years. We definitely see combat, but we also see another rules subset: nonweapon proficiencies, or skills.
Over the edition changes, the system for handling this has been narrowed down, from a large list of various skills, to a narrow list of less than 20. So 4e provides us the most "streamlined" view of what PC's need rules for, outside of combat: what characters actually do.
The Four Things Skills Do
When you look at the recent list of skills, you can see they all attempt to answer the question of "Is what I try to do successful or not?" The things that they measure actually fall into four camps:
- Can I overcome this obstacle while I move? (Stealth, Endurance, Acrobatics)
- Can I get this NPC to believe me? (Diplomacy, Bluff, Intimidate)
- Do I know this factoid? (Nature, History, Perception)
- Can I do this combat stunt? (Heal, Acrobatics, Bluff)
You can see from there, how we get four pillars: Exploration, Interaction, Discovery, and Combat.
But how do we cut it down to three?
Discovery Is Not a Roll
One of the questions that the skills answer is automatically very binary: "Do I know this factoid?" The only possible answers are Yes and No, and it immediately relies on your die rolls rather than your character's actual world history and knowledge.
This can be handled in a more "acquisition" fashion. Your character, if they know something about magic, can automatically know about basic facts, and learning more things requires you to interact with the world.
So this is how we get rid of Discovery: it's not something we need to roll for, it's either something your character does already know, or it's something your character can find out by investigating.
Special Senses & Expertise
You may notice that I put "Perception" (aka Spot and Listen) in the bucket with Discovery. If discovery isn't a roll, how do you describe a character with heightened senses, such as an elf or a ranger? And how do you accomplish sneaking against characters who don't roll to oppose you?
Generally speaking, this can be handled through extra traits. An elf may have the Heightened Senses quality that allow it to know more about its environment than others, while a cleric might have the Religion quality that gives them religious knowledge about any situation. It simply happens: if they have the trait, they know more.
Stealth, then, becomes a way to work against the senses. Your Stealth roll becomes something that must beat a more static DC based on the sense you are deceiving. Low DC's may move silently, moderate DC's may avoid sight, and higher DC's may avoid detection by heightened senses, or even by scent, or tremor-sense!