Before you can configure a site to allow anonymous access, the associated web application must have anonymous access enabled through central administration. If the web application is set through central administration to allow anonymous access, you can control what parts of your site are new visible to anonymous users. Once the web application is configured for anonymous access, you can return to Permissions page of the site.
You can select Setting Settings -> Advanced Permission -> Settings -> Anonymous Access entire site/all lists/nothing at all. Additionally, you can control the visibility of an individual lists or library through its permission settings. To do this, go to the lists, Settings -> Anonymous access - > Add Items/Edit Items/Delete Items/View Items. This combination of site-level and list level configuration gives you a good deal of control over what parts of the site can be accessed anonymously.