The focal plane of most lenses is carefully designed to coincide perfectly with the sensor, such that the two are coplanar. Tilt-shift lenses essentially rotate the focal plane of the image such that it only properly intersects with the sensor along one line, leaving the rest increasingly out of focus.
As to why that makes things appear miniature, that is more of an optical illusion which is easy to demonstrate. Close one eye and hold one finger from each hand very close to your open eye, but at different distances. Focus on the finger that is farther away and, as you do so, try to be conscious of what is happening to the image of the closer finger and also the background. You should be experiencing this as a narrow depth of field where only the finger you are looking at is in focus and things that are farther and closer are blurry; this is similar to shooting photos with a large aperture. In the natural world, your brain only ever experiences such narrow depths of field when things are very close to your face. Thus, when you apply such a depth of field effect to a scene, no matter how large it is, your brain assumes it must be very small relative to you because otherwise there would be no such effect.
As to why that makes things appear miniature, that is more of an optical illusion which is easy to demonstrate. Close one eye and hold one finger from each hand very close to your open eye, but at different distances. Focus on the finger that is farther away and, as you do so, try to be conscious of what is happening to the image of the closer finger and also the background. You should be experiencing this as a narrow depth of field where only the finger you are looking at is in focus and things that are farther and closer are blurry; this is similar to shooting photos with a large aperture. In the natural world, your brain only ever experiences such narrow depths of field when things are very close to your face. Thus, when you apply such a depth of field effect to a scene, no matter how large it is, your brain assumes it must be very small relative to you because otherwise there would be no such effect.
-Quora
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