I always thought of the lines as elliptical narrative. He was distressed at being left by his love and has decided to enlist in the navy. He is taunted by the lads of the wood, who ask him how many strawberries grow in the sea. He answers them with the only taunt he can think of: "how many ships sail in the forest?" But he's aware his answer is slightly hollow as he does not truly love ships, hence the tear. This realization is what makes him, finally, wish for death.

I realize that my interpretation may be idiosyncratic, but this is how it's always fit into the song for me. I do of course realize that it also adds the sense of futility of the traditional impossible tasks verses.