Jasmine allows you to define behaviour specifications, or specs for short, for your software and tests to determine whether your software meets your specification. The whole process is automated, meaning that any tests you write with Jasmine are tests that you no longer have to spend time conducting manually. You can run these tests whenever you like, giving you feedback for the smallest of code changes. The more you automate, the less work you have to do. The more you test, the greater insight you have into changes you make to your code.
Jasmine follows the principles of Behaviour Driven Development, or BDD for short, which starts with behavioural specifications as the basis for all your tests. If you use user stories in your software development process, behaviour specifications will look familiar to you as they contain natural language definitions of the behaviours you are testing for. Dan North, creator of BDD, has an excellent introductory article, and I recommend it as background reading if this is a new topic for you.