Generally the difference between a consultant and a contractor is kind of diffuse, but basically a consultant has more autonomy and is expected to offer advice and guidance based on their experience, while a contractor is expected more to just implement a plan given to them. But as I said it's very diffuse and many people use the term contractor and consultant interchangeably.
As to what it requires, literally just that you can convince someone to pay you money for you to give them advice. Often a consultant will have a lot of experience in a specific area and will be brought on by companies that need help and expertise in that area for a specific project, but don't want to hire an expert full time.
There are also consulting companies that employ people and hire them out to other companies as consultants. At which point you just get a regular salary from your employer and the company you are hired out to pays your employer for the hours you work.