Don’t forget about the “Help” button in the top-right of the WP admin screen!
The Help refers to the Settings Reading SubPanel page in the Codex which says the following:
Posts page – Select in the drop-down box the name of the Page that will now contain your Posts. If you do not select a Page here, your Posts will only be accessible via other navigation features such as category, calendar, or archive links. Even if the selected Page is Password protected, visitors will NOT be prompted for a password when viewing the Posts Page. Also, any Template assigned the Page will be ignored and the theme’s index.php (or home.php if it exists) will control the display of the posts.
In other words, the page you choose in that drop-down will act as nothing more than a placeholder and its contents and template are ignored completely (only the title is used). Use home.php or index.php instead.
Also see Creating a Static Front Page.