Well, this verse tells us unanswered prayers will soon cease and you you'd start getting what you've been asking for. "Will he keep putting them off?" [Luke 18.7] strongly insinuates that God eventually gives what we pray for if we don't give up. The passage adds how God will see to it (imagine that? He'll make sure) that they get justice "and quickly," though "keep putting off" and "quickly" seem two contrasting ideas.
Well, just believe it.