Does each brand get its own page on my store?

Yes. Each brand has its own page on your store, at /brand/ followed by the brand's slug, for example /brand/nike. It shows the brand's Description above the title and the brand's products.

To check or change the slug, go to Products → Products, click Brands, open the brand and look at Slug. Click Save after any change.

The page only works while the brand's Status is Active. If you set the brand to Inactive, its page shows "not found". That is useful for brands you no longer stock.