Rashi comments that the word “nefesh,” soul, is not mentioned in regard to any Korbanos Nedavah, free-willed offerings, except for a Korban Minchah, meal offering. This is because usually the one who brings a meal offering is a poor man. Hashem says that He considers the poor man’s offering as if he had offered his soul as a korban. Simply put, this is because the poor man, regardless of the minimal value of his offering, contributed relatively more than his wealthy counterpart. Consequently, his korban represents a more significant sacrifice.
Horav Eliyahu Meir Bloch, zl, supplements this idea.. When the wealthy man brings his korban, he feels that his large gift earns him total penance. The poor man, however, knows that he gives very little and that his korban pales in quantity, compared to that of the rich man. He feels that he has not given enough to Hashem. He, therefore, offers his nefesh together with his korban as a way of entreating Hashem to accept the little that he offers. There is a sense of humility that accompanies the poor man’s korban. He feels that he does not give what he should. The emotion and the attitude that goes hand in hand with the korban transforms it into a supplication to Hashem. One should feel that he never fully gives Hashem what he should–only what he can.