Abstract general definition: In discourse, it refers to the impossibility of inquiring about an interlocutor's opinion on something without introducing that something first.
This might appear trivial and meaningless at first, but instances of the problem can often lead to frustrating situations. Imagine the following: you are not sure whether you should tell your friend that she has a large piece of dark-colored food stuck between her front teeth. After all, she might feel horribly ashamed upon you pointing out this fact. So, you would like to ask the question, "Would you be ashamed if I told you that you had a piece of licorice stuck between your front teeth?" yet herein lies the problem - to ask this you need to give away precisely what you needed to ask the question about in the first place.
Other common manifestations of the (In)eviton problem include: "What would you say if I told you I am in love with you?", "What grade would you give me if you knew I copied this paper off the Internet?", "Should I tell you what your friend said to me about you?" etcetera.