The value passed to check the box is often "Yes" and "Off" - However, this is only the default value and it can be changed from "Yes" to almost any value at all (this is controlled by the export value of the document, as pointed out by others).
If you are looking to procedurally get the on/checked state value (which you will need to reliably set this checkbox as checked), it is contained in the appearances "AP" dictionary of the field. That dictionary should contain another dictionary "N", and each key is one of two values for the checkbox. The first key will be the unchecked value (usually "Off") and the second key will be the checked value (usually "Yes"). How you do this entirely depends on the API.
If you use pdftk from the command line, you can see what the expected values are using the command dump_data_fields: Eg.
pdftk document.pdf dump_data_fields
Will show something like this:
---
FieldType: Button
FieldName: basform
FieldFlags: 0
FieldValue: No
FieldJustification: Left
FieldStateOption: Off
FieldStateOption: basic_forms <---- Checked value expected by FDF
Here we can see that the checked state is actually expecting "basic_forms" and not "Yes". I believe the other state is always "Off", but that may depend on the language your program is using (the default "Yes" value certainly does).