Jenkins is an automated tool/server used for various automated tasks related to building, testing and delivering software.
Here we mostly use it for the building and testing parts, it can be integrated into various systems too, for us GitLab, where it detects CS errors and outputs them in Merge requests.
There are also LOADS of plugins for PHP Test coverage, phpmd, phpcs, phploc etc. etc. guhh.
Per Branch this is the information you can see about it in our Jenkins instance (example BookingEngine master branch)