"One can only hope" is what we call a Colloquialism. It can be expanded like this based on the speakers conversation: Example 1 Speaker 1: If we buy this ticket we could win the prize. Speaker 2: One can only hope. Typically meaning many things in four short words. Speaker 2 is expressing to Speaker 1 the only way they can influence the situation. The two speakers can just hope or wish that they will win the prize. In other words, there is nothing physical that the speakers can do to influence the outcome of the situation. Example 2 Speaker 1: The doctor said I might not be sick. Speaker 2: One can only hope.

The speaker wants something to happen, or wants something to be true, but it is not in his or her control. So he says, "one (short form for "a person") can only hope" that it happens as they want it.