In general testing is comparing actuals versus expected when having as objective to control that the system respects the requirements defined by the client.
Testing should satisfy the need for information on the differences between the object and the defined requirements. But more than that, we need to know the causes behind the problems and identify and help to resolve those causes.
So based on the analysis, the causes will be determined, the problem will be consistently solved, and future risks can be foreseen. In summary, the quality of the system will be improved. A principle of quality, also sustained by Agile, is that it is better to foresee than to solve. A high severity defect solved in early stage, during build for example, will cost less than a minor production issue.
While in manual testing the tester executes manually the test going through the test cases, in automation testing he makes use of separate special software (test tool own built code) to control the execution of tests comparing the actual outcomes with predicted outcomes. Tests so carried out, can be run repeatedly, at any time of day with several advantages: