I put my installation into a folder called /members on my server. When I go to the main members page and I click either Signup or Login, it seems to have a /members/member/index or /members/member/signup directory. Am I correct to assume that those aren't actual directories and somehow Amember redirects to particular pages/files? Because those directories aren't on my server. I'd like to get everything to /members but now I'm just being picky I think.
Yes these are not real directories. all amember requests are handled by /amember/index.php script, so all requests that go into /amember/ folder will be redirected to index.php by mod_rewrite. You can see rewrite rules in /amember/.htaccess file.