As you want cells to change based on whether the item is due for calibration this month, next month or more than a month away you need to use conditional formatting.
Start with formatting the cells Green.
Then use Conditional formatting to change the cell colours as the difference between due date (the value in the cell) and the date today changes.
Click on one of the cells with a calibration date
Click Format - ConditionalFormatting...
Under Condition 1 Select Formula Is
In the box enter the following formula:
Select formatting and change the pattern to Red (you may also want to change the font to white)
Now select Add and under Condition 2 select Formula Is and enter the following Formula
Select Format and a yellow pattern with black text
If the date in cell B3 (in this example) is in the same month as today's date, the first formula will evaluate to TRUE (note true is not in double quotes), and will format the cell Red. If false, i.e., date is not in current month, the second formula is evaluated. The second formula tests if the date in B3 has the same Month as today + 1 month, i.e., next month. If the formula evaluates to TRUE the cell is formatted Yellow.
If both formulas evaluate to FALSE, the original cell formatting is unchanged, leaving the cell green.
Once one cell is setup, copy the cell, then Paste special - formats to all the other date cells.
If you Paste Special - Formats to other cells with equipment descriptions etc. they should also change to the same colours.
You could add a third condition for equipment that has passed its due date.