His wife had initially accused him publicly of having an affair with a Pakistani journalist (Mehr Tarar) who had interviewed him once. She presented as evidence private emails from Tarar to Tharoor, which were quite explicit in their implication that there was a romance between them. They both strongly denied this, and Tharoor claimed that his email account had been hacked.

Later, Tharoor's wife admitted to having written and sent the emails herself using an email handle that closely resembled that of the journalist. She claimed that she had done it because she "knew" that the journalist was stalking her husband. This was apparently based on the one interview and a glowing piece that she had written about Tharoor in the Lahore Times. In his wife's own words "Our accounts have not been hacked and I have been sending out these tweets. She is stalking my husband. And you know how men are. He is flattered by the attention… I will not allow this to be done to me. I just can't tolerate this." She also accused the journalist of being a Pakistani spy.

That's what he meant when he said that his wife was "unwell". It doesn't seem likely that there was an affair, but who really knows. After she made this admission though, it wasn't much of a threat to his political career. And it would have been stupid for him to kill her in the midst of all that media attention. There is still controversy over whether she died of a drug overdose (suicide), poisoning, or a medical condition, so the case is far from closed.