The speaker begins the poem by describing their hands, which reflect traits inherited from both their father and mother. The speaker doesn't merely say that their hands look like their parents' hands; instead, the speaker claims that their parents are "in" their fingers and palms, as though both parents maintain a physical presence within the speaker's body.
The parallel grammar of this opening line emphasizes the fact that the speaker is a combination of their parents—that they're equally part of their father and mother. Note, too, how a caesura breaks the line cleanly in half, separating the speaker's parents from each other:
My father's in my fingers, but my mother's in my palms.
Looking at their hands makes the speaker happy because it helps them feel close to their parents. Their hands are a reminder that the speaker's parents "made" them, and thus that the speaker belongs to a family lineage.
This opening stanza also establishes the poem's form. "Genetics" is written in iambic pentameter, for the most part, a meter in which each line contains five iambs (poetic feet that follow an unstressed-stressed syllable pattern). The meter isn't perfect—the first line has two extra iambs (making it iambic heptameter) and the second line has an extra unstressed beat at its end:
My fa- | ther's in | my fin- | gers, but | my mo- | ther's in | my palms.
I lift | them up | and look | at them | with pleasure—
I know | my pa- | rents made | me by | my hands.
These variations are relatively minor and, overall, the lines echo the clear da-DUM da-DUM rhythm of a heartbeat.
"Genetics" is also something called a villanelle, meaning its first and third lines will be repeated (albeit with some variation) at the ends of the following stanzas. Keep an eye out for this repetition.