Use the adjective tidy for something that is neat and clean. If your desk were more tidy, you would be able to find your computer.
Tidy (or tidy up) also means “to clean up” and is also a noun for a container for small objects, like scraps or sewing materials. These senses of tidy have a formal or even old-fashioned note. (We’re more likely to say clean, organize, or bin now in everyday conversation.) A less informal use is as an adjective, meaning “large.” If you can put the word tidy before your profit or the sum in your bank account, it’s a good thing.