"Would" can be the past-tense of "will", but when it is used about a future event in this way, it is for hypothetical situations or conjecture.
Do you think that he will come?
This would be appropriate in situations where you are waiting for somebody, perhaps because you have invited them to attend something, and you were asking someone for their opinion on whether the person will, or will not come. Although their answer might be partly conjecture, it is an assessment of the invitee's response to a tangible invitation.
It is common to speak about hypothetical situations as if they were in the past, using verbs in the past tense (eg "Do you think he would come if I asked him?")
Do you think he would come?
This would be appropriate if you were asking someone's opinion on a hypothetical situation - for example, if you were considering inviting someone to attend and event (but had not yet invited them). You are asking if the person would hypothetically attend if you invited them.