What's JSHint?
JSHint is a JavaScript syntax checker.
It can find lots of errors in your code and enforce your preferred style (spaces, not tabs!) JSHint originated as a fork of JSLint and was designed to be less "opinionated" and more configurable than its predecessor.
Advice: Use ESLint
While JSHint was a great tool for its day, ESLint is what you should be using now. ESLint is far more configurable, checks for more issues, and has really easy-to-understand documentation. Most importantly, ESLint supports the newest JavaScript standards like ES6.
CodeKit 3.0 supports JSHint mostly for backwards-compatibility. As of 2016, ESLint is the industry standard in JavaScript syntax checkers. You should move to it immediately.
That said, this recommendation is in no way a condemnation of JSHint or its developers. The JSHint community simply decided not to support next-generation JavaScript, which puts them at a huge disadvantage. Over the years, JSHint has improved countless websites and pushed the world forward. Anton Kovalyov (its creator) and all the people who work on it deserve our thanks.
Using JSHint
Please see the help page for ESLint. Both tools are very similar and the instructions for ESLint mostly apply to JSHint as well.