Note that your second sentence should be "What makes you think that?
As well as being the past tense of "will": "I will come to the party." / He said he would come to the party", would can express the possibility, probability or likelihood of something.
What would make you think that? = What is likely to make you think that?
Would is used in these ways:
1 - I wish he would stop doing that. - Regret about somebody's behaviour.
2 - Would you help me, please? - Polite request.
3 - He said he would do it tomorrow. - Reported speech (past tense of will).
4 - I would rather you didn't do that. - Expressing a preference about an action.
5 - And every day he would go jogging. - Past habit.
6 - Well, he would say that, wouldn't he? - Commenting on somebody's typical behaviour.
7 - Would you help me with this? - Indirect question/
8 - Would you like to have more coffee? - Polite offer.
9 - I would imagine that he is about 30 years old. - Softening an opinion you are not sure about.
10 - He wouldn't help me. - Refusal in the past.
11 - One day he would become president. - Future in the past.
12 - If he had heard the weather forecast he would have started earlier. - Third conditional.
13 - Be careful! It would break if you dropped it. - Predicting a high probability.
14 - etc.
Best Answer
The speaker is apologizing for not understanding something that you said and is politely asking you to rephrase it (say it again but in a clearer way).