This button is shown when you are a user in a group with the right to "Delete Products from Filterview" and the total number of products in the current filter is less than or equal to 1000.
The number of items in the current filter can be seen next to the search field indicated in parentheses.
Checking user permissions
To check user permissions, go to the admin panel 'User Groups' and search for 'Delete Products from Filterview'. In addition, check that the logged in user is in this user group.