The kohanim- holy priests- were commanded to offer a mincha offering twice daily, called ‘minchas chavitim.” The kohanim had to pay for this offering with their own money. The commentators explain the reasoning behind this, they say, “First adorn yourself, then adorn others.” In other words, one should work on developing himself and his character traits before helping others. Although we have a social responsibility to help others and reprove them when they are transgressing, we must first work on improving ourselves, by constantly surrounding ourselves with learning and developing our middot-character traits. Only after we have ‘adorned ourselves’ can we ‘then adorn others.’
Moreover, the offerings the kohanim brought were of flour and oil, which were considered the sacrifices the poor man would give (seeing that was all he could afford). In other words, Hashem was making a point to show, that a poor man should not feel embarrassed that he is giving such a low status korban-sacrifice because the kohanim-holy priests- were giving the same sacrifice.
Additionally, since the high priest was commanded to offer sacrifices for his sins before atoning for the sins of the entire Jewish nation, Hashem wanted to portray that even the high priest, who is so close to Hashem, may also come to sin, but he moves pasted his feelings of embarrassment and still repents. This should serve as an example for us, although we may not be as ‘holy’ or close to Hashem as the kohanim-high priests- may be, nevertheless, we should not let the embarrassment we feel for the sins we have committed prevent us from repenting and rebuilding our connection with Hashem. If the holy kohanim- high priest-acknowledge their own sins, but still find the strength within to repent, we too should follow their example and find the strength within ourselves and rebuild our severed connection with Hashem.