"When a person (nefesh) will bring a korban mincha, his offering shall be of fine flour" (Vayikra 2:1). Rashi comments that the Torah uses the term nefesh to describe one who brings a korban mincha because typically only a poor person offers such a cheap korban. The Torah is hinting to the fact that the monetary value of the korban is irrelevant. Even if the animal that a wealthy man offers is more expensive than the flour of the poor person, nevertheless the poor man's korban is just as beloved. Hashem considers it as if he sacrificed his nefesh - his soul.
But if the Torah wanted to highlight the value of the poor man's korban, then it should have used the term nefesh in the context of a bird offering. After all, the bird offering is even less expensive than the korban mincha. Even the smallest bird is sufficient to be brought as a sacrifice, while a korban mincha must contain at least forty eggs worth of flour as well as a measure of oil and spices. The flour offering might not be worth as much as an animal, but it certainly is worth more than a small bird. Why then does the Torah make a point of using the term nefesh specifically in the context of the flour offering?
The Panim Yafos (the author of the Sefer Hafla'ah) answers that what is special about the sacrifice of the poor man is not the material that he offers but his lowly spirit - his ruach she'falah. The poor man's humility is symbolized by flour, which comes from plant life (tzomei'ach), as opposed to animals and birds which are living creatures (chai). The Torah identifies the poor man with a korban mincha to highlight that it is the lowly spirit of the poor man that makes his korban so beloved to Hashem.
Chazal comment (Sotah 5b) that one who has a humble spirit is considered to have brought all types of korbanos, as is hinted to in the posuk, "Zivchei Elokim ruach nishbara - a broken spirit is equal to multiple korbanos. (Tehillim 51:19)" What's more, Chazal add, his tefillah is readily accepted, as the possuk continues, "Hashem will not despise a broken and humble heart."
Why does a humble person deserve such special treatment? Chazal say (Sotah 5a) that the Torah was given on Har Sinai because of its modesty. All the other mountains felt that since they were tall and prominent, they were worthy to be the site of kabbolas haTorah. But Har Sinai was quiet. (see Midrash Tehillim, Shochar Tov, 68:15) And precisely for that very reason, because Har Sinai was reserved and humble, it was chosen as the place upon which the Torah was given.
The Shechina always seeks out a lowly place. Hashem connects with someone or something that is humble. Chazal comment that one who walks with an erect stance - one who is arrogant - pushes away the Shechina (Kiddushin 31a). Hakadosh Boruch Hu says about one who is haughty, "I cannot live together with him in this world (Sotah 5a)." But one who is humble in spirit draws the Shechina closer. "I live in exalted heights and holiness," says Hashem, "but I am with the despondent and the lowly of spirit" (Yeshaya 57:15).
This is why one who is humble is considered to have brought all types of korbanos. The word l'hakriv means both to sacrifice and to draw close, because bringing a korban is a way to come closer to Hashem. The more humble a person is, the more Hashem is drawn to him. The intimate connection that a humble person enjoys with the Shechina is similar to the closeness felt by one who has brought all kinds of korbanos.
Nowadays, when the Beis Hamikdash is no longer standing, tefillah is in place of korbanos. Tefillah is a vehicle through which we connect with Hakadosh Boruch Hu, who is the mekor ha'bracha - the source of all blessing. By acting with humility, we cause the Shechina to draw closer to us, and we make ourselves worthy recipients of Hashem's blessings.