The main reason is that the lens isn't perfect.
Ideally a properly focused image of a point light source would be just a point. That doesn't happen in real life for several reasons:
- The lens glass isn't perfectly transparent. There is always at least a little bit of milkiness. By far, most of the light thru a lens is refracted as intended. However, a small fraction of any light hitting the lens is scattered.
- Diffraction. When light passes close to the edge of a baffle, it is actually bent a little. This effect is only significant up to about a wavelength or so from the edge. The aperture for adjust the f-stop in your camera is such a baffle. Most of the light passes well away from the edges, so goes straight thru. However, there is a thin ring just inside the aperture where the light is bent. That light ends up somewhat spread out in the final picture.
Since the thin ring inside the aperture is always the same thickness (since it is a function of the wavelength of light), the ring is a larger fraction of the whole at smaller apertures. This effect is usually what limits the smallest apertures of macro lenses. In macro shots, you usually want all the depth of field you can get. Stopping down the lens helps, but at some point the whole image becomes less sharp. I have a 60 mm macro lens where this effect is quite noticeable at f/64 with ordinary scenes that don't have a few very bright spots.
- Light bounces around between elements of a lens. This is a small fraction of the total light, so normally you don't notice it.
- Light bounces around inside the camera. The sensor isn't perfectly black. Even if you could focus a perfect point on some area of the sensor, that would illuminate the inside of the camera, which would in turn diffusely light other parts of the sensor.
All these effects are small. The vast majority of light ends up on the sensor where you intend. However, some fraction of every bit of light entering the lens ends up on every other sensel where it's not focused on. Most of the time, this fraction of light from other parts of the scene is so small that the intended scene light hitting a sensor at any one location swamps this diffused light.
Taking a picture of a few very bright light sources with everything else black is the worst case, and these effects add up to be visible. If you were to expose so that the lights themselves were properly exposed, then the surroundings would look black. You are seeing the spillover because the lights themselves are so over-exposed that they are clipped, and the spillover therefore a higher fraction of the maximum value.