The reading of the passage from Ex. 12 indicates that the months begin from Nisan, when the Israelites were redeemed from Egypt and became a people.
From the practical point of view, it is a reminder that Pesach is imminent and that we should make ourselves well aware of the laws of chametz and matzah, which are detailed in this reading.
There is actually a link between HaChodesh and the portion for this week, Tazria, since both deal with new birth – HaChodesh with the birth of a people and its calendar, and Tazria with the birth of a child.
In both cases the new birth comes as a consequence of pain, and just as a woman often says that the pain of childbirth was worth it when she sees her baby, so the Jewish people might say they were able to handle the enslavement in Egypt because of their faith that it would be followed by a new era.