God gave the firstfruits of Israel's blessings to the priests as provisions for them and their family.
GOD provided special blessings for the Levitical priests. Among these blessings were the first and best of Israel's produce and reproduction.
8 Again the Lord spoke to Aaron, “I give you charge over the firstfruits from all the things sanctified to Me by the children of Israel; and I give these things to you and your sons with you as your share. This shall be an eternal ordinance. 9 So let this be yours from the sanctified holy things of the offerings: from all their gifts, from all their sacrifices, from all their trespass offerings, and from all their sin offerings, and from whatever they return to Me—let all these holy things belong to you and your sons. 10 In a most holy place you shall eat these things; every male shall eat these things. It shall be holy to you.
11 “This also shall be a firstfruit for you from their gifts—from all the deposit offerings of the children of Israel—I give these things to you, and to your sons and daughters with you. This shall be an eternal ordinance. Everyone who is clean in your house shall eat these things. 12 The firstfruits of oil, wine, and grain, all their firstfruits, whatever they may offer to the Lord, I give these things to you. 13 Whatever first ripe fruit is in their land which they bring to the Lord shall be yours. Everyone who is clean in your house shall eat these things. 14 Every devoted thing in Israel shall be yours.
15 “Everything that first opens the womb of all flesh which they bring to the Lord, from man to cattle, shall be yours; nevertheless, the firstborn of men you shall redeem, and the firstborn of unclean cattle you shall redeem. 16 Now as for its redemption at the age of one month, the rate is five shekels according to the holy shekel (that is, twenty obols). 17 But the firstborn of young bulls, the firstborn of sheep, or the firstborn of goats you shall not redeem; they are holy. You shall pour out their blood towards the altar, and offer their fat as a burnt offering for a sweet aroma to the Lord. 18 Their meat shall also be yours, just as the breast of the deposit offering and the right shoulder are yours. 19 Every choice part of the holy things which the children of Israel offer to the Lord, I give to you and your sons and daughters with you as an eternal ordinance; it is an eternal covenant of salt before the Lord with you and your seed with you.”
(Numbers 18:8-19 OSB)
The priests worked hard serving the Israelites according to the functions GOD prescribed through Moses. GOD rewards honest work, so He gave the firstfruits of Israel as a blessing of payment for the priests' service. These things would sustain the priests and their families. As offerings made to GOD, these firstfruits should have been the best the Israelite had to offer. Therefore, the quality of the contents of these offerings should have been high.
The firstborn child and the firstborn unclean cattle were to be redeemed—paid for, not unlike the concept of a tax. Since all firstfruits belonged to the priests, fundamentally, the first child and unclean cattle also belonged to the priests. However, since neither human nor unclean animal could be eaten (thereby providing physical sustenance, as clean animals could), the child and the unclean animal was to be "bought back" (redeemed).
Israel's redemption payment concept was also a shadow of things to come, as the Messiah would provide the redemption payment for sin to buy back sinners from the penalty of the law of sin and death. (The law of sin and death said if you sin, you die.) This payment, however, would be offered in righteous, sinless blood unto death.