In "Meeting at Night," the speaker is a male. In the first stanza, the speaker is making his way through the water/sea. The descriptions of the landscape/seascape indicate that it is at night. As the speaker travels over the water, the landscape is still/asleep.
And the startled little waves that leap
In fiery ringlets from their sleep,
The speaker awakens the sea as he travels. He awakens nature; this will parallel the next stanza when he awakens the person he's going to meet (possibly a lover, maybe even some kind of secret rendezvous). Note the sexual imagery as well: the "pushing prow" of his ship and the "slushy sand" that the prow pushes into when he reaches the shore, thus "quenching" his speed.
In the second stanza, the speaker must still travel a mile on land. He arrives at a house, taps on the window pane, and inside someone (presumably a lover) lights a match for a candle or lantern. In joy and fear, (she) whispers ("less loud") than the sound of their two hearts beating together. Remember the parallel: in the first stanza, he awakened the waves (nature) and here he awakens her, awakening her human/sexual/loving nature.
(Browning's poem "Parting at Morning" is the companion piece to this poem and describes the speaker's departure the next morning.)