After eight days had passed, it was time to circumcise the child; and he was called Jesus, the name given by the angel before he was conceived in the womb.
It's what you do.
On the eighth day the male child is circumcised. That's the procedure. Even if your child is the Son of God.
Amidst all the weirdness and completely not-normal stuff that happened in the time leading to the birth of Jesus, and after the rather dramatic angel intervention and shepherd invasion of the night of the birth, the next thing we get is this simple sentence about first-century Jewish parents doing what first-century Jewish parents do.
One of the things that stands out as odd about what we know of Jesus's life is this yawning gap between birth and age thirty. Aside from the episode in the Temple when Jesus was twelve, we skip from this infant/toddler (more on that later, on day 12) to the thirty-year-old Jesus showing up to be baptized by John the Baptizer. Childhood, young adulthood...<crickets>. Nothing.
Not that everybody was willing to accept this. If you delve into the non-canonical material about Jesus, stuff that came out decades or even centuries afterwards, you get some really bizarre accounts about bizarre, willful, even cruel things done by the child Jesus. Modern authors are not immune to the temptation to "fill in the blanks" about Jesus' life, either.
We stink at not knowing, or more precisely at accepting that we don't know. There are some occasions where that's a good thing; I'm glad that doctors and researchers didn't settle for not understanding cancer. But there are occasions where it leads to unhealthy and even destructive behaviors, wild unfounded speculation, and incredibly bad religion.
What's also interesting in the case of these non-canonical accounts, though, is the apparent need to make Jesus's childhood, well, "special." The miracles and the power have to start showing themselves at a young, even very young age. The possibility that Jesus just had a childhood -- a reasonably calm, normal childhood -- is apparently unacceptable.
The thing that appeals to me here is the utter normalcy of what the verse describes -- what any male Jewish child would have had done on day eight -- juxtaposed with the reminder of how not-normal things had been up to that point ("the name given by the angel..." -- not everybody has that experience). At some point, if you're Mary and Joseph, you've got to get on with raising the child.
What do you do when the Son of God poops his swaddling clothes? You get new swaddling clothes, or clean the old ones, and clean up the child. Normal.
The child has to be nursed. The child has to be burped. And after eight days the child has to be circumcised.