Hey Les,
Travis-CI is just the integration point, it runs in the cloud, not on a client machine. The actual tests would be some perl testing framework, whatever is chosen, and those tests could be launched locally by the developers as well. Ideally the test-running would be built into the code base, but you could get a little creative and run them however worked best for your processes.
Travis-CI will get kicked off whenever someone submits new code to GitHub, and would run on a VM in the cloud (provided by Travis-CI) for free. Travis will run whatever testing framework is configured for the project and then report the results right on github.
I have used Jenkins, it's a nice tool and has been used by many projects. However, the Travis-CI integration into GitHub just makes it hard to beat. Many of the projects Lars mentioned used to use Jenkins and have since switched to Travis due to it's capabilities.
David