The poem's speaker is the titular mower, someone who, in poet Andrew Marvell's day, would cut grasses with a scythe. This mower, apparently working at night, addresses some glow-worms (a.k.a. fireflies) directly. This is an example of apostrophe; the glow-worms can't respond to the speaker, but this direct address conveys a sense of kinship and intimacy.
Right from the start, the mower is full of praise for these little creatures. He deems them nature's own "living lamps" and calls the bioluminescent light they cast "dear," or precious. The gentle alliteration of "living lamps" and "light" lends delicate beauty to the poem, those lilting /l/ sounds like pretty sparks brightening up this opening line.
The glow-worms, the speaker continues, provide the light for the "nightingale" to stay up late, studying her music. The humble bugs illuminate the summer evening, and in doing so allow the bird to sing her "matchless song." Nature, in this scene, exists in exquisite harmony, its diverse creatures coming together to create peerless beauty.
Note how sound patterning works almost like a melody here, with hushed sibilance and humming /m/ consonance and alliteration deftly woven throughout the lines:
The nightingale does sit so late,
And studying all the summer night,
Her matchless songs does meditate;
The nighttime scene is filled with lush, delicate beauty.
And yet, already, the speaker subtly foreshadows the poem's melancholy ending. When he calls the nightingale's song "matchless," he means, on the one hand, that her music is beautiful beyond compare. But "matchless" might also mean that the bird has no partner, no beloved with whom to share her song. The speaker's word choice might subconsciously reflect his own broken heart.
This opening quatrain also establishes the poem's form. The poem is written in iambic tetrameter, meaning its lines contain four iambs: poetic feet that follow an unstressed-stressed syllable pattern, as follows:
Ye liv- | ing lamps, | by whose | dear light
The night- | ingale | does sit | so late,
And stud- | ying all | the sum- | mer night,
Her match- | less songs | does med- | itate;
It's arguably possible to hear that first foot as a spondee (two stressed beats in a row, "Ye liv-). For the most part, though, the meter is steady, its gentle da-DUM rhythm creating a soothing, even hypnotic atmosphere. The alternating ABAB rhyme scheme adds to the poem's familiar, predictable music. It's almost like there is a misty, moonlit spell cast over the poem.