There's a lot of small details and choices that combine together to make a world feel big. Each small thing isn't enough to do it on its own, but with enough details working together the player will feel that sense of "bigness". Most of these details are rules and expectations that humans have subconsciously internalized, things that we don't necessarily think about but have taken as true.
The most common detail of "bigness" is visible size. Most areas in video games are already built larger than they would be for a real person of that size. Having buildings that are scaled larger than normal in video games contributes to a sense of grandeur. The SWTOR Jedi Temple on Tython, for example, is apparently built for giants. There's no way that normal-sized humanoids could live or operate comfortably in a space that large, but the purpose isn't a real living space, it's to convey a sense of enormity and grandeur to the players who enter that space.
The amount of time it takes to navigate the area also contributes to the sense of how large a place is. If you think about traveling in real life, the metric of travel time is the most commonly used to determine how far away something is. This means that making travel time take longer actually makes something feel bigger, because our brains tell us "the longer it takes to get there means the further away it is", even if it isn't actually that far away. Look at how long it takes the player to approach the Colossus in this animation. It makes the colossus feel so much bigger because it takes so much longer to reach it.
We also often use tricks like forced perspective in certain places in order to make things feel bigger. If we have unreachable areas (e.g. cliffsides, mountain faces, etc.) that are still visible, we can use visual tricks to fool our brains into thinking things are further away or larger than they actually are. Without a reference point that can break the illusion, our minds will fill in the gaps by constructing its own consistent world view - that castle looks this big, so it must be this far away. The illusion above is only broken because we know roughly how tall a human is, so either the humans are giant or the buildings are tiny.
These various tricks (plus others that I haven't talked about) work to stitch a cohesive experience together in the player's mind. Your brain is being shown many things that have all subconsciously meant "big" to it before, so it assumes that its internal rules are still correct and the thing is big.
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