If you archive a test, it no longer shows up on your homepage. You usually archive a test if you have created a test for demo purposes, or if some test is very old and you don't need it anymore. It will then show up in the Archived Tests section and your homepage won't look as cluttered.
If you want to permanently remove a test from your account, you can delete the test from the archived tests section. The test will not show up anymore on your account, but the test results data will still be available.