When a foreigner or illegal alien (non-US citizen) comes to the USA to have a baby for the purpose of making the baby a US citizen. The baby becomes a US citizen giving the illegal alien/foreign parent and their family grounds to come to and stay in the US and become eligible for government benefits. Also called a "jackpot baby".

an anchor baby is a term used for when an illegal alien mother-to-be hops the border into the country right when she's ready to deliver the baby, and gives birth to the child inside the country, in order to gain legal residental status in the country, due to her child automatically being a citizen of that country, by virtue of being born in the country.

What your girlfriend hopes to achieve by "forgetting" to taker her pill, thus guaranteeing that you'll have to spend the rest of your now ruined life with her... or that you'll have to run from the law forever to avoid child support.