Looks like the header navigation is rendering as a site map rather than as a dropdown menu.
From the developer console, it doesn't look like you are failing to load any required style sheets (which is one cause of this sort of problem).
I would look at the headernav area and navigation block and make sure you are using the right template for the navigation block, or that you have not simply included the wrong type of navigation block (some themes come with their own theme specific navigation blocks).
Just what this template or block is will be theme dependant, so if the answer is not obvious, you need to ask on the support page for your theme.
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From the developer console, it doesn't look like you are failing to load any required style sheets (which is one cause of this sort of problem).
I would look at the headernav area and navigation block and make sure you are using the right template for the navigation block, or that you have not simply included the wrong type of navigation block (some themes come with their own theme specific navigation blocks).
Just what this template or block is will be theme dependant, so if the answer is not obvious, you need to ask on the support page for your theme.