The question asked how the law is relevant but the first answer simply asserts that it is not relevant. I am therefore adding an answer that I think is more responsive to the question's assumption.
I think that you can argue (especially if you are pro-choice) that the bill is intended to further the argument that a fetus is a fully human life. True, it does not actually say this. But have a look at this statement by a pro-life group from 2002
The law guarantees that every infant born alive enjoys full legal rights under federal law, regardless of his or her stage of development or whether the live birth occurred during an abortion.
“This important legislation ensures that every infant born alive -- including an infant who survives an abortion procedure -- is considered a person under federal law,” the President said before signing the bill. He added, “Today, through sonograms and other technology, we can see clearly that unborn children are members of the human family, as well.
(I added the bold face to parts that I thought are important...)
In Roe v. Wade, the Supreme Court put forth the argument that fetuses in the first (and to some extent the second) trimester are not really viable outside the mother and that states may not regulate abortions in those trimesters as much as they regulate abortions of fetuses deemed to be viable.
This law, especially given the statements above, is arguably a move towards the idea that any fetus, at any stage of development, is part of the "human family" and should therefore not be aborted.
The Born-Alive Infants Protection Act of 2002, redefines the words "person, human being, child, or individual" in the United States Code to include "every infant member of the species homo sapiens who is born alive at any stage of development." Born-alive means that the infant was completely expelled from the mother, no matter at what stage of development and has a beating heart, pulsation of the umbilical cord and a defined movement of the voluntary muscles. So even if a mother has decided to abort pregnancy, but the child is born such that it can be saved unless it is denied medical aid that will lead to its death, it has to be given the required medical aid to save its life.
This Law does not try to stir up the argument of the mother’s rights versus those of the unborn child but instead is meant to ensure the rights of a completely born baby that can live if it is provided the right medical care. Doing this also does not interfere with any of the rights of the child’s mother.