A highly unusual event unfolded during the Passover celebration when a massive crowd of Israelites partook of the sacred sacrifice while in a state of ritual impurity. This vast multitude [מצודת ציון, ביאור שטיינזלץ] consisted primarily of individuals from the tribes of Ephraim, Manasseh, Issachar, and Zebulun [מצודת דוד]. The sheer size of this group held significant legal weight. Because the majority of the congregation was impure, the Passover offering was legally permitted to be brought in a state of impurity [מלבי״ם].
However, the primary approach among commentators is that the people consumed the sacrifice improperly. Eating from a holy offering while impure is a severe offense that carries the penalty of spiritual excision, a punishment not applied to merely touching the sacrifice [רד״ק]. Because the Passover offering can only be eaten by those who pre-registered for it, the impure individuals were forced to consume it themselves and could not appoint pure substitutes to eat in their place. To minimize the impurity as much as possible, pure Levites stepped in to slaughter the sacrifices in the Temple courtyard on behalf of the people [מצודת דוד].
In the wake of this transgression, King Hezekiah offered a prayer for atonement. On a basic level, he prayed on behalf of the people who ate the sacrifice while impure [רד״ק]. He asked that although their bodies lacked the required purity, God should focus on their good intentions and their prepared, worthy hearts [מלבי״ם]. According to this approach, his plea for God to atone connects directly to the people's sincere inner preparation [רד״ק].
Alongside this perspective, another approach suggests that the improper actions and the subsequent prayer also addressed the king's personal failings regarding the calendar. Hezekiah had improperly added a leap month to the year for several reasons: he did so specifically because of the people's impurity, he declared the leap year during the month of Nisan itself, and he violated the rule prohibiting a king from sitting on the council that calculates leap years [חומת אנך].
The actions of the king and the people were deeply intertwined. Hezekiah declared the leap year to grant the people enough time to purify themselves before Passover. Had they succeeded in doing so, his calendar adjustment would have been considered valid after the fact, requiring no special prayer. However, because the people ultimately remained impure and ate the sacrifice in that state, Hezekiah's leap year declaration was retrospectively proven useless. Consequently, the king was compelled to pray and seek atonement for himself, having violated the calendar laws without achieving his intended goal [מלבי״ם].