The Membership Details link on the WishList Member Widget (also know as the Login Widget) allows members to edit their profile.
The Membership Details link directs a member to their profile so that they can edit their password, etc. if desired.
The title of this link can be edited for both logged in and logged out users in the Appearance > Widgets section of WordPress.
If you want to remove this link, you can do that in the Advanced Options > Global Defaults > Other section of WishList Member.
You would need to Disable the “Members can update their user info” option.