The correct interpretation would be:
to show that his speaker is in love and trying to persuade their intended with beautiful words.
In this sonnet, the speaker is comparing the beloved to a summer's day, emphasizing the beauty and pleasantness of the beloved. By using the metaphor of a summer's day, the speaker is trying to convey that the beloved surpasses the qualities of a typical summer day.
The phrase is used to create a contrast between the fleeting nature of a summer day and the enduring beauty of the beloved. The speaker is employing poetic language and imagery to convince and persuade the intended recipient of their affection.