GitHub is a web-based interface that uses Git, the open source version control software that lets multiple people make separate changes to web pages at the same time.
With GitHub, you can create public repositories (open source projects) to store your work or collaborate with others. You can also make private repositories for free (3 collaboraters per repository).
Integrating GitHub with Jira you can, attach pull requests, issues and commits to cards including all the information, you can configure GitHub to run unit tests, labels from GitHub get updated on Trello boards and track the entire pipeline from within Trello.
You can use Jira to track your entire development pipeline, and use GitHub for Pull Requests and code review. It's free for private repositories and organizations (even if yours it's not an open source one). It has a good and intuitive User Interface which makes viewing information and reading code easier. It's the go-to solution for hosting open source projects.