In Nikox Coolpix compact camera there are two video modes for 1080/25p so they have the same number of pixels, aspect ratio and number of frames per seconds. The only difference is bitrate 15.7Mbps and 10.4Mbps. So what is the difference between that, what additional information is stored using 15.7Mbps?
The higher bitrate will store more detail in your video. Most video cameras use file compression to throw away parts of the image that they think the viewer won't notice, in order to reduce the size of the file. Even though both files would contain the same number of pixels, areas of low detail would be compressed more in the lower bit rate image.
Lossy compression of files is a trade-off between image quality and file size.
Wikipedia has a good example of what happens - the two files below are the same resolution, but one is much more heavily compressed.