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A homography matrix basically represents the relationship between two images that are on a planar surface.
Taking your image mosaic project as an example, say you have 2 images that you need to 'merge'. You need to find the homography relationships between the key-points of Image A with the key-points of Image B. After you get this relationship, you can then warp the images in order for them to successfully 'merge'.
This openCV example should explain it better -> http://docs.opencv.org/doc/tutorials/features2d/feature_homography/feature_homography.html
I have answered to the best of my knowledge, to the extent of what I personally understand. Hope I helped.
