Jasmine is a behavior-driven development framework for testing JavaScript code. It does not depend on any other JavaScript frameworks. It does not require a DOM. And it has a clean, obvious syntax so that you can easily write tests.
Karma is essentially a tool for testing which spawns a web server that executes source code against test code for each of the browsers connected. The results of each test against each browser are examined and displayed via the command line to the developer such that they can see which browsers and tests passed or failed.
Jasmine and Karma are usually used together to perform Unit testing or integration testing.
Protractor is an end-to-end test framework for Angular and AngularJS applications. Protractor runs tests against your application running in a real browser, interacting with it as a user would without depending on other tools for performing the same. Check out how it works here.
References:
Jasmine Documentation
Karma – How it works?
Protractor