They allow status tracking of the test cases, i.e., to document and evaluate if, when, how often, and with which result ("passed", "failed") a test case has been executed.
They help the test manager to plan the tests and to remain informed about the status of hundreds or thousands of test cases.
Advanced test management tools support requirements-based testing. For this purpose, they allow the capture of requirements or to import them from requirements management tools and the linking of them with the test cases needed for validation.
Source: SWT Foundations
Andreas Spillner, Tilo Linz: Software Testing Foundations, A Study Guide for the Certified Tester Exam, dpunkt.verlag.