Spenser's Sonnet 75 is part of a sonnet sequence and presents on element of his love for his lover. In short, the element involved here is his desire to immortalize his lover and their love.
The speaker first tries to do that by writing her name in the sand on the beach, but the waves wash it away. He tries a second time, but the tide washes it away (first quatrain).
His lover then tells him he is vain for trying to immortalize something that is mortal (2nd quatrain).
He counters, insisting that his poetry will immortalize her (3rd quatrain).
He concludes with the idea that when death has killed all the world, their love shall live, and will renew life (closing couplet).
There's a bit of interpretation for you. I'll let another editor pick up from there.
By the way, the speaker was correct. At least partly: we're still reading his poem.
You will find many similar poems among the Elizabethans, particularly Shakespeare's sonnets. The idea here is that while our lives are fleeting, art will last (forever?). The speaker, which Spenser freely admits is himself, is walking on the beach with his true love--his wife, of course. As a romantic gesture he writes her name in the sand, but it is quickly washed away. She tells him that he is silly for trying to immortalize her in writing (the sand), but this gives him the opportunity to specifically say that she and their love for one another will live on through his poetry. He tells her "My verse your virtues rare shall eternize," and makes reference to the transcendent beauty of art. Considering that we are still reading this poem and can appreciate the love he feels for his wife well over four hundred years later, he seems to make a good point.