You shall bring an offering all seven days… (Leviticus 23:8)
There is a mitzvah to bring a korban musaf – an additional sacrifice – each of the seven days of Passover. (Remember, Biblically-speaking, Passover is only seven days even though nowadays we observe eight days outside of Israel.) The musaf consists of two bulls, a ram and seven lambs, as a burnt offering, plus a goat for a sin offering. (The burnt offerings were entirely burned – hence the name! – the sin offering was partially eaten.)
The reason for the extra offering, in addition to the two regular daily offerings, is to impress upon us the significance of the day. A person is influenced by his actions, so actually having extra offerings sends a much more powerful message than just telling people, “Hey, you know what? Today is special!”
Nowadays, the korban musaf is reflected in the additional prayer service we say on holidays, which is also called “musaf.”
This mitzvah applied in Temple times. It is a mitzvah for the entire community but the responsibility to carry it out fell on the kohanim, whose job it was to offer the sacrifices. It is discussed in the Talmud in tractate Menachos (see, for example, 44a-45b, 49a-b, 87a-b, et al.). It is codified in the Mishneh Torah in the seventh chapter of Hilchos Tamidin and is #43 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.