Jenkins is a Continuous Integration server.
Basically Continuous Integration is the practice of running your tests on a non-developer machine automatically everytime someone pushes new code into the source repository.
This has the tremendous advantage of always knowing if all tests work and getting fast feedback. The fast feedback is important so you always know right after you broke the build (introduced changes that made either the compile/build cycle or the tests fail) what you did that failed and how to revert it.
If you only run your tests occasionally the problem is that a lot of code changes may have happened since the last time and it is rather hard to figure out which change introduced the problem. When it is run automatically on every push then it is always pretty obvious what and who introduced the problem.