Letting user choose from 2 options for QGIS Processing script input parameter?

If you are not limited to QGIS v2.8 (your screenshot points to v2.8 documentation), you can install a newer version. For example, in QGIS v2.14 you have a selection parameter type available (see the docs):

enter image description here

You can use it in this way in the header of the script, separating options with a semicolon:

##Units=selection Millimeter;Centimeter;Meter

And later in the script you can get the chosen value in this way:

if Units == 0:
    # User chose millimeter
elif Units == 1:
    # User chose centimeter
elif Units == 2:
    # User chose meter

For reference, here you have an example script.

Germán Carrillo's answer is the most convenient. A possible alternative (if you're stuck with QGIS 2.8) could be to:

  • Use a string which allows the user to enter the units they want to use:

    ##units=string mm
    if units == 'mm':
        # Do something
    elif units == 'cm':
        # Do something
    elif units == 'm':
        # Do something

    Text units

  • Or use three boolean checkboxes:

    if Millimeter == True:
        # Do something
    elif Centimeter == True:
        # Do something
    elif Meter == True:
        # Do something

    Checkbox units