In order to see the Master Page menu option in the “Look and Feel” Sites Settings section in SharePoint 2010, you have to activate the SharePoint Server Publishing Infrastructure. There are two features that need to be activated in SharePoint
These features must be activated at the web site level and not by using the Central Administration Web Application. This can cause some confusion because these settings are available in the Central Administration tool.
First, navigate to the website that where you want to activate the Publishing feature. Next, Select: Site Actions>Site Settings
Now Select, Site Collection Features from the Site Collection Administration section:
In this section you want to activate the SharePoint Server Publishing Infrastructure
Go back to the Site Settings page and select Manage Site Features from the Site Actions section. This time you need to activate SharePoint Server Publishing.
Once this is activated the Master Page option will be available in the Look and Feel section for the Site Settings:
Its important to remember that this must be set up at the site level.