One of the most important characteristics of the key points is its repeatability under different geometric transformations and also lighting. Repeatability ensures that if, for example, you have two images of the same scene, at different sizes and also with a different angle of rotation, the vast majority of key points in both images will coincide and, in this way, you can make a " matching " between both. In the SIFT algorithm these key points are invariant to translation, rotation and scale; for each key point the neighborhood is coded (in a radius proportional to the scale of the DOG operator) using histogram of gradients of 128 components, in this way each key point (x, y) will have associated a vector of 128 components, this vector is known as "descriptor". And what is the usefulness of this?
Object Recognition: given a gallery of images of different objects, a set of descriptors can be stored for each image. When a test image arrives, its descriptors are extracted and compared with the stored descriptors. For this, noma-L2 or classification sparse representation is generally used.
"Partial face recognition: An alignment free approach"
Scene Reconstruction: if you have several images of the different parts of a scene, these can be joined, based on the key points, to reconstruct an image of the whole scene.