Heroku is a cloud platform that allows companies to host their Rails applications without owning the physical infrastructure. Some key advantages are variable costs that scale with usage and high flexibility. Deployment can be challenging due to limitations on configurations and reliance on a third party. The Heroku stack provides automatic scaling through dynos and add-ons, and uses Git-based deployment where code is pushed to build application slugs. While not suitable for all large applications, Heroku is recommended for new simple projects due to its low cost and ease of use.