This formula uses the IF function to check for "complete" in column C. When a cell contains "complete", IF returns
which displays a checkmark when the font is "Wingdings". When a cell contains any other value, IF returns an empty string (""). Note the IF functions is not case-sensitive.
Important: cells in column D must be formatted with the "Wingdings" font for this to work.
Excel's CODE and CHAR functions allow you to work with ASCII codes for characters directly in a formula.
You can use this same approach to display any symbol or character you like with a formula.
On a Mac
On a Mac, use 159 to get a checkmark with Wingdings:
Plain text checkmark
You can also try just a plain text checkmark like this: ✓
=IF(A1="complete","✓","") // plain text
The display on Windows and Mac versions of Excel is more primitive, but it gets the job done without using Wingdings.
With conditional formatting
You can also use Excel's built-in conditional formatting icons to show a checkmark, but you don't have much flexibility.
For a complete run-down on conditional formatting with formulas, with many examples, see this page.