I have a checkbox that I want to control by referencing a cell, let's say cell A1. If the value of cell A1 is "Completed", I want the checkbox to be marked, if it is not "completed", I want the checkbox to stay unchecked.
By default checkboxes linked to cells show either TRUE or FALSE. If you want to control checkboxes thru text/values entered in a cell, you can do that using a simple macro.
But if you just want to display checkbox value as "Completed" etc. then you can either use formulas or custom cell formatting.