The concept of a fully-diluted basis is not difficult. A fully-diluted basis just means the assumption of the highest potential amount of common stock a startup will have outstanding, regardless of vesting provisions and assuming all options and other securities like convertible notes are converted into common stock. That is, assume the highest share count possible.
I’ve seen it defined in legal documents in the following way:
“Fully-Diluted Basis” shall mean the assumption that all options, warrants or other convertible securities or instruments or other rights to acquire Common Stock or any other existing or future classes of capital stock have been exercised or converted, as applicable, in full, regardless of whether any such options, warrants, convertible securities or instruments or other rights are then vested or exercisable or convertible in accordance with their terms.
The definition of fully-diluted basis matters especially for founders in financings. Typical VC financing deals will calculate the Series A share price on a fully-diluted basis, and the investors have an incentive to capture as much shares as possible in the definition of fully-diluted basis. The larger the amount of shares calculated by the definition of fully-diluted basis, the lesser the Series A share price.