Spot metering measures the brightness of a subject only in a very small part of the image and ignores all the rest.
The spot used for measuring is as small as indicated in the picture on the right to allow a really accurate selection. But it can very a bit between cameras and Canon e.g. offers two types of exposure metering that differ in the size of this measured area.
The place of this spot used for metering can be in the center of the image or follow the points used for autofocus.
This is dependent on your camera and possibly also on settings in your camera.
The spot where you have taken the exposure will be rendered as medium gray.
If you want this place to appear brighter or darker you have to dial in an additional exposure compensation.
In case you have chosen an extremely bright spot, e.g. including the sun or reflections of direct sunlight your camera can differ and be smart enough to make the spot white without a correction.