This is a restriction imposed by Apache. It is designed to prohibit ambiguity in determining which access controls apply to the directory.
Assume your public directory contains a subdirectory called example. If you access it via /example, you have not entered that directory. That means that the .htaccess file from your public directory would be applied, but the .htaccess file inside the example directory would not. However, if you access it via /example/, then you have entered the directory and both .htaccess files will be applied.
Now, assume that your public directory's .htaccess file allows all visitors and has directory indexing enabled. Assume that your example directory's .htaccess file allows only visitors with a certain cookie set and denies directory indexing. In this case, if it were allowed, visiting /example would produce a listing of the contents of the example directory while visiting /example/ would produce an access denied error or demand for authentication.
To prevent the confusion and security issues that such conflicting behavior would create, Apache detects attempts to access directories without trailing slashes and automatically issues a redirect to the same URI with the trailing slash appended. That way, you never have to worry about the scenario in the preceding paragraph.
Although you can't stop people from typing one in by hand, make sure you don't use invalid directory URIs internally on your site because they require this extra redirect, thus making your site appear slower.
If you find that these redirects are not using the site alias that you want, for example, if they redirect you to example.nfshost.com instead of www.example.com, then you may need to adjust your site's canonical name settings.