Diminish means to make smaller or lesser. If you cover a lightbulb with a dark lamp shade, the light from the lamp will diminish.
It can also mean become less important. Once the light has been dimmed, its role in lighting the room is diminished. If you look at diminish, you see 'minis' which comes from the Latin word minus, as in subtraction. Other words that share this root are miniature and minuscule, all of which mean something that is small, or at least smallish.