To make open-world exploration more "meaningful" is a tall order, but as a general rule I think the best thing to go for is to ensure that any discoveries provides the player with the appropriate sense of satisfaction; in other words, the proper "reward".
Of course, this doesn't mean that the "rewards" are beneficial items (equipment) or even fun gizmos; a great looking vista, or perhaps even a small ruin to wander about in (perhaps littered with a few chests with small sums of gold, depending on the game), is adequate. One common (and effective) approach is finding something which implies there's a history to the locale, even if there's no connection to the primary story; for example, a tomb of a long-forgotten king or where a last-stand (lots of bodies) had taken place. Still, one shouldn't disregard the journey to the discovery at the end either, but there almost certainly should be something at the end of it; that something just doesn't necessarily have to be of material value.
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The other bit to take into account is how something is actually discovered, and for that there are four basic methods:
The Locked Door
The simplest, and least rewarding, of the discoveries; in fact, it's not really a discovery. Something "extra", but immediately apparent and clearly optional (if you want to bother to find the key). Functional for more material rewards, but doesn't really encourage exploration; just being thorough, so that you get all the loot.
The Secret Passage
A basic discovery, but it still allows the player to find something which isn't immediately obvious. An extension of the current location, where the entrance blends in with the rest of the architecture; finding these comes down to either random chance or looking for tell-tale signs, neither of which comes with the appropriate "build-up" to a bigger discovery. However, this could also be the start of something much larger as well...
The Path to the Unknown
This one is the start of something good, quite literally. The player finds a path, perhaps behind "the locked door" or "the secret passage", but they don't know where it leads; so they follow it, finding stuff along the way. Perhaps it starts as small, beautiful locations; but leads to something much larger in the end, such as a the hidden ruins of a city. Anyhow, the path is visible... but not the destination. Of course, the path should be nice to look at and around; but curiosity of what lies within is the real motivator at this point.
The Unreachable
An inverse of "the path to the unknown", as the location you want to reach (or more specifically, the exterior of it) is quite often in plain sight... but the road of how to get there isn't immediately apparent. Most of these tend to be viewed from a lower location initially, and the idea is get higher up. The idea is to encourage the player to poke around until they find the path which gets them to the location and subsequently allow them to explore the interior. The start of the path to the location can be quite far away as well, but once the player clue's in that it leads to something they could see before it will spur them onward
Of course, to get the best results a game should use a variety of techniques and combine them in a variety of ways; a huge draw about exploration is the idea you'll find something "new and interesting", so it shouldn't be all the same approach or the same thing at the end.
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To comment on the "making worlds smaller" (or even the inverse), I don't think that really has the desired effect. Larger worlds allow discoveries to be hidden by the sheer size of the world, but that's half-cheating; the above techniques still have to be employed, more travel time to a destination doesn't encourage exploration. However, making the world smaller doesn't automatically solve the solution; that pushes for more of the smaller discoveries (which aren't quite as fun), larger ones just become harder to fit into the game ("the unreachable" in particular). Larger game worlds are definitely an asset for any exploration-focused game, but it has to be used properly
Fast-travel is something of an issue to exploration as well, as it allows the player to bypass many of the potential secrets of the game; even if optional, the convenience tends to be a bit too alluring. Fast-travel to previously accessed locations only definitely helps, and short-cuts to major locations should be left out; another way to encourage exploration would be to place obstacles on the main path (perhaps even impassable ones), to half-force the player to find or "discover" another way around.