Creating elbow room
The Oculus Quest tracks multiple movement types to create an immersive virtual reality experience. The headset tracks your head's movement in six directions (up, down, left, right, forward, and back) and the touch controllers track your hands' movements. Put together, these allow you to look around environments and swing your arms away to interact with games.
Many Oculus Quest games require you to move your hands quite a bit to play. For example, Beat Saber has you swing your arms to slice through music beats with virtual lightsabers. Other games require boxing or other similar movements. To play these you'll need enough room to swing your arms freely while standing.
Because the Oculus Quest has sensors built into the device and doesn't rely on external towers, a PC, or anything other than Oculus Quest itself, you don't need to dedicate as much space as you would for the Oculus Rift or HTC Vive. That being said, you still need enough room play games without smacking a wall, your desk, or another person. It's best to clear out space and make sure that it's clear of any objects whenever you put on the device.
More room, more fun
At launch, the Oculus Quest won't support arena-scale tracking, but that will come with a future update. Arena-scale tracking maps out massive areas and remembers where items so you can mix virtual and actual reality. With it, you can run around an arena of up to 4,000 Square feet (or potentially more) and the Oculus Quest will remember where physical objects are and place them into games so you won't run into them while wearing your headset.
It's unlikely that you'll have 4,000 square feet free in your house but the same tracking works with smaller spaces as well. Once arena-scale tracking rolls out for the Oculus Quest you might want to clear some more space in your home, especially if you have friends or family who also own an Oculus Quest.