Some commandments are famous for their grandeur. This one is famous for its neighborliness. Targum Pseudo-Jonathan on Exodus 12:4 addresses a perfectly mundane problem: what if your family is too small to finish a lamb in one night? The Torah does not want leftovers of the Passover offering to sit until morning. So if your household numbers fewer than ten people — not enough eaters to handle a whole lamb — you join your nearest neighbor.
The Aramaic number of ten is not in the Hebrew of Exodus 12:4, but the Targum adds it because this is the working rule in rabbinic practice. A minimum of ten was the expected count for a havurah, the fellowship group that would share the Pesach. If you were short, the solution was not to shrink the lamb but to widen the company.
This is a commandment about the architecture of community. The Pesach offering cannot be eaten alone or left half-unfinished. It requires company. The Targum's phrasing — "he and his neighbour who is nearest to his house" — is strikingly local. You do not go searching for the right host across town. You open the door and ask the family next door.
The rabbis later saw in this the seed of the entire concept of tzibbur, the public quorum of ten. Even on the most personal night of the year, Israel was not to eat alone.
Takeaway: The Torah engineered Pesach so that no family could escape into privacy. You had to eat this meal with company, or not at all.