The Torah forbids entering the mikdash or eating the meat of a korban in a state of impurity (so-called טומאת מקדש וקדשיו) .
Someone who transgresses in error (beshogeg) gets forgiveness through repentance and a sin offering see Vayikro 5 (2) and Rashi there.
In addition, the Torah obligates various offerings to atone for these acts.
1) The Kohen Godol confesses this sin on his own ox for himself and his brother kohanim see Vayikro 16 (11) and Rashi there .
2) The “he-goat for Hashem” obtains the people's atonement for this Vayikro 16 (15) and Rashi there .
3) The mishnayos in Shevuos 1 (4 – 7) describe the various offerings that also effect atonement for טומאת מקדש וקדשיו. The Tannaim argue over the atonement of the additional offerings for Rosh Chodesh and the Sholosh Regolim: the factors involved seem to be when, if at all, the person became aware of the sin and if a separate offering is needed for eating as opposed to coming into the mikdash.
Why does the atonement for impurity in the Temple take so many different forms?