The speaker of "A Dream Within a Dream" is one of those really philosophical dudes. He's the kind of guy who likes to pick up things and stare at them, searching for their deeper meaning. Okay, that's not really our thing, but hey to each his own, right?
While a lot of us have probably never really stopped and thought deeply about the nature of reality (especially while at the beach), our speaker sure has. He once met some woman who told him that all that we see or seem is just a dream within a dream, nothing more. Before he leaves her, he kisses her and tells her that she was not wrong to think that; he even agrees with her before he takes off for good.
But he's not the kind of guy who's just going to accept something without conducting a few little experiments. After his departure, he's not so sure about the whole life-is-a-dream deal, so he spends some time grabbing handfuls of sand at the noisiest beach he can find to try to convince himself that the world was actually real and not just an illusion. The sand keeps slipping through his fingers, though, which is more than a little exasperating.
Our speaker, however, is not the kind of guy who gives up, or despairs, though he might cry out to God a few times and start crying like a baby. Even after this little incident with the sand, he still has his doubts. Instead of declaring that life is just a dream within a dream, he questions whether or not that was really the case, hoping someone will prove him wrong.