I don't know if my understanding is correct, but I will assume "ripen" means as much as "expire" in this context, otherwise the whole thing would be complete bollocks
Convertible shares are quite common in the business world, especially when working with startups.
For investors they offer a great deal. If the company does well they can be 'converted' into regular shares. So if a company skyrockets to success, they get a large piece of the money. However, the the company does not do well but still survives in business, the shares are treated as a loan that is due at the end date. Finally, if the company fails and goes bankrupt, the convertible shares are given high priority during asset liquidation, so the investor will get a relatively large amount back.
When Zenimax bought id, Carmack (a co-founder) was due $45M of the $150M purchase price since Carmack owned about 1/3 of the company. Carmack decided to take a bunch of it in convertible shares. The lawsuit says currently Carmack has convertible notes for $22,559,047.77, or about $22.5M.
The actual lawsuit papers include the text of the convertible note contract, you can read them here if you're interested in the details, pages 11 through 18.
When convertible shares "ripen", it means the payment becomes due "no later than June 23, 2017". He has the option of cashing it out earlier, but Zenimax MUST pay by then. He has chosen to cash it out early, which is his right in the contract.
In the text of the contract it says he can get a specific number of shares, or get the cash equivalent of buying at $45/share, or require the full amount as cash with no interest charged. (It also has provisions for changes in stock value like stock splits and such.)
This is also complicated by Zenimax's recent testimony in the previous case. Carmack owns about 5% of Zenimax, and while on the stand in the case the CEO testified under oath the value of the company was about 2.5 billion dollars, almost double what they said on paper earlier.
The lawsuit even made a crack about that in paragraph 16, with that the price: represents a substantial discount from the valuation that the company’s CEO, Robert Altman, recently swore to under oath. So while he is asking for the $22.5M, he probably could reasonably demand $125M based on the testimony of the first trial, and the judge would have a high chance of granting it; when someone testifies one number to one judge in his favor and testifies a different number to a different judge that is also in his favor, the judges really don't like that. So since he already testified the $2.5B number, Carmack could probably force him to that same valuation in this case.