A neat person or thing is tidy and well-organized.
When someone says something is neat, they often mean that it's attractive and pleasing to look at. You might hear, "The decorations for the party were really neat!" In this case, neat means visually appealing. But when describing a place or situation, neat can also imply orderliness - like a neat desk with all papers in their proper folders. Some people use neat to describe someone's personality too; they mean that the person is reliable and organized, not messy or complicated.
How common is "neat"?
Word neat is considered uncommon in modern English. It has a balanced usage among all categories: speech, fiction, newspapers and academic texts.
Definitions
noun
An artificial intelligence researcher who believes that solutions should be elegant, clear and provably correct. Compare scruffy.
adjective
Clean, tidy; free from dirt or impurities.
Example: My room is neat because I tidied it this morning. She has very neat hair.
Free from contaminants; unadulterated, undiluted. Particularly of liquor and cocktails; see usage below.
Example: I like my whisky neat.
Conditions with a liquid reagent or gas performed with no standard solvent or cosolvent.
Example: The Arbuzov reaction is performed by adding the bromide to the phosphite, neat. The molecular beam was neat acetylene.
With all deductions or allowances made; net.
Having a simple elegance or style; clean, trim, tidy, tasteful.
Example: The front room was neat and carefully arranged for the guests.
Well-executed or delivered; clever, skillful, precise.
Example: Having the two protagonists meet in the last act was a particularly neat touch.
Facile; missing complexity or details in the favor of convenience or simplicity.
Example: Courts should not reduce this case to a neat set of legal rules.