The first two lines of "On My First Daughter" introduce the setting and subject of the poem. In saying "Here lies," the speaker evokes the image of someone standing at the head of a grave, where a body might be buried. He follows this up by noting that whoever lies in the grave is there to "each her parents' ruth," with "ruth" being an older word for "sorrow." In other words, the poem opens with an image of parents grieving for their dead daughter.
In the second line of the poem, the readers learn who the grave belongs to: Mary, the child alluded to in the previous line. Readers can also assume that the speaker himself is one of these parents, and in fact it is widely understood that this poem was written after the death of Jonson's real-life daughter Mary in her infancy.
However, the "father" in line 4, who readers now know is the speaker of the poem, notes that there's something making him feel less sorrowful ("less to rue"). Why? Because, as stated in line 3, he knows that the gift of his daughter's life was granted by heaven, and he was lucky to have her on earth for as long as he did. Now, her life has been called "due"—a rather cold comparison, like a bank loan being due—and therefore her soul had to return to heaven. The repetition of the word "heaven" in line 3—technically an example of diacope—underscores the father's thinking: heaven granted life, and as such heaven can take it away. In this instance, the speaker's faith is a source of comfort (his daughter's soul is now in heaven) while also a source of bitterness (she was called back far earlier than he would have liked). Ultimately, though, his belief in heaven helps to relieve his sorrow, if only slightly.
In terms of form, these four lines consist of two sets of rhyming couplets, a pattern that will continue throughout the poem (and indeed is common for elegies like this). The rhymes are perfect end rhymes—"ruth"/"youth" and "due"/"rue"—allowing the poem to flow smoothly and the reader to focus on the sorrow being expressed. These lines are also end-stopped, their grammatical phrases each aligning with the end of lines themselves (note that, especially for older poems like this, punctuation is not always a clear indicator of end-stop or enjambment). This adds to the poem's sense of quiet grief, of the speaker trying to contain his own sorrow via methodical reasoning about death and the afterlife.
The poem's meter is generally iambic tetrameter, meaning there are four iambs—poetic feet with an unstressed-stressed syllable pattern—per line. Already though, it's clear that this meter isn't perfect. The first line can be scanned as opening with a spondee, meaning it has two stresses in a row:
Here lies, to each her parents’ ruth,
This draws emphasis to the poem's opening phrase, underscoring the finality of Mary's time on earth. The next line then opens with a trochee (stressed-unstressed), before falling back into steady iambs:
Mary, the daughter of their youth
The child herself thus again interrupts the metrical regularity of the poem. Subtly, then, the hiccups in the meter—which notably appear when the speaker refers to his daughter's name and gravesite—reflects the weight of the speaker's grief, the way it imposes itself on his attempts to comfort himself with logical reasoning about religion and the afterlife.