Link for earthy body brand looks like this
<a href="/?brand=715 ">Earthly Body</a>
This looks like, the design try to trigger a search based on brand and it fails and hence redirecting to home page.
brand is a product attribute that is used in in admin side to set brand of a product. If so, you need to make that attribute first visible in search. For this you need to
Catalog > Manage Attributes.
Make it visible in search.
For more details you can check this links LINK 1, LINK 2.
An another work around would be make
brand as a "invisible category" and display that category when the brand link get clicked. For this
Create a new category with name "brand" - parent category that holds individual brands
Create sub categories for brands. They should be individual brands
Associate each product with corresponding sub category.
Create logic to display brands. (in frontend)
Whatever my be the way that you adopted, you need to edit the template file that provides brand links according to the way you implemented the brand view. Means you need to change the
href part like wise.
Hope that makes sense !