The Torah is nothing if not a manual for order and doing things properly. Nowhere is this more obvious in the ritual of the Tabernacle and sacrifices.
At each stage of the sacrificial ceremony the officiating priest must change his clothes. The process of sacrificing is of course a messy business. So is separating the different parts of the animal bodies. Someone had to carve them up. In some cases, hundreds of animals were involved. Teams of priests were on shift.
Some parts were washed and placed on the alter. In some sacrifices the animal was completely burned. In others, edible parts were taken to be eaten by the Priests. In other sacrifices, they would be taken by the donor to be eaten by him and his family or shared with others. Some fats and parts and skins and offal were separated for other uses. It is not surprising that clothes needed regular cleaning and changing.
But the Torah also insists that a noble and significant function of the priesthood is to remove the ashes from the alter in between sacrificial cycles. This too required changing clothes. But it is regarded as an honor.
We take cleanliness for granted. But in most societies, it was not. Particularly amongst the poor. Seeing the importance of cleanliness, of sweeping up after one, in the tabernacle and later in the temple will have sent an important message to the wider community. That sweeping up, helping around the house, cleaning one’s clothes, these are tasks that if they are good enough for the priests, ought to be good enough for the common person too.