The Checkout Core Page is a dynamic page. The fields displayed change based on the payment settings configured, whether the person viewing the page is logged in or not, as well as the embedded information provided from purchase links.  So the account section and associated fields (first and last name, email, password, phone number) will only show up on the core checkout page if someone is not already a member or if the member is logged out.  So if you are viewing the page as admin, or if an already registered customer is making a purchase, this section will be hidden. 

If the account section is not visible to a non-member (when logged out), then you should double-check that the [MM_Form_Section type='accountInfo'] and [/MM_Form_Section] SmartTags are surrounding the account section on your checkout page.