The idea of going on a clothing diet is about having a simple wardrobe - 1. just a few essential items (e.g. the six items of less movement - sixitemsorless.com), or 2. a simple color palette ( e.g. Jobs always wore black turtlenecks and blue jeans), or 3. essentially pick a uniform (e.g. Timoni West, who has decided to make do with a set of a hoodie, a t-shirt, a tank top, leggings, a skirt, socks, and shoes).
In essence, adopting a clothing diet means you are giving up the traps of excessive consumerism - at least that's the idea. Steve Jobs may have been a simple dresser, but he sure built a consumerist cult around expensive, not totally necessary devices. But, that's a different story.