As the other answers have mentioned, Swagger provides a way to define and document your API endpoints, methods, responses, errors, and more. It does not do any sort of automated testing out of the box.

There are a few tools that can read a Swagger definition to created automated tests, though:

• Assertible is a tool where you can import your Swagger spec to automatically create tests and assertions for every endpoint and method. You can then set up monitoring, post deployment testing, and alerts. (Read the blog Testing an API using Swagger). It has a free plan with options to upgrade for more tests.
• swagger-test is an NPM package, if you're looking for something to integrate with your code. I haven't personally used it, but it does look active and useful.
• Dredd is another really cool open-source tool that will automate testing your Swagger spec against a live backend. This is also a CLI too, and it works with API Blueprint in addition to Swagger.

There's others as well, because Swagger provides a good common language for API developers there's some great tools that are written on top of it.

Another answer mentioned to check out the Commercial Tools page on swagger.io, which has some more hosted services (free and paid).

Full disclosure - I'm one of the co-founders of Assertible and would love to hear your feedback if you get a chance to use it.