Do they ever explain the contract marriage? What is the ex-wife's reasoning for wanting a one year marriage for Gong Yoo, How does it help the ex-wife in any way?

 SyedRahman:

Do they ever explain the contract marriage? What is the ex-wife's reasoning for wanting a one year marriage for Gong Yoo, How does it help the ex-wife in any way?

She is taking a twisted revenge on ML. Yes, they tell it all in the show.