Leviticus 27 describes the laws regarding the dedications of people, animals, and houses to G-d. The dedication involved sacrificing the item in question to G-d. In some cases, such as in the dedication of animal, the item could be literally sacrificed. However, in other cases, such as a person, there is a general principle that the sacrifice was substituted for a monetary payment given towards the service of G-d.
Leviticus 27:9 reads:
וְאִם בְּהֵמָה אֲשֶׁר יַקְרִיבוּ מִמֶּנָּה קָרְבָּן לַיהֹוָה כֹּל אֲשֶׁר יִתֵּן מִמֶּנּוּ לַיהֹוָה יִהְיֶה קֹּדֶשׁ
"And if they bring a (kosher) animal as an offering, any part from which they give will be holy unto G-d."
The Talmud (Arachin 5a) relates that a man could actually offer an individual part of an allowed animal by entering into an agreement with someone else who wanted to purchase the animal for a sacrifice. The owner of the animal would end up offering that certain part while being financially compensated for the remainder. Here, we see that dedicating a kosher animal literally means sacrificing it to G-d.
However, Leviticus 27:11 mentions that in the case of a unclean animal, the priest will determine what the value of the animal is. As Rashi discusses, the unclean animal will then enter into the Temple treasury where it will be available for purchase by another party. And if the owner of the unclean animal wishes to redeem it, he will the full price plus one fifth added. In this case, we see that the item cannot be dedicated to G-d's service, so instead a compensation takes its place.
Leviticus 27:2 deals with the dedications of people (souls):
דַּבֵּר אֶל בְּנֵי יִשְׂרָאֵל וְאָמַרְתָּ אֲלֵהֶם אִישׁ כִּי יַפְלִא נֶדֶר בְּעֶרְכְּךָ נְפָשֹׁת לַיהֹוָה
"Speak to the children of Israel and say to them: "When a man expresses a vow regarding the value of lives to G-d."
The Talmud (Arachin 20a) interprets the phrase בְּעֶרְכְּךָ נְפָשֹׁת to refer to vital organs of the body. Hence a man could dedicate his heart or liver to G-d. However, this was interpreted as meaning giving an amount corresponding to the value of his life. Again, as in the case of dedicating an unclean animal, we see that dedicating one's life meant in practice giving a certain compensation to the Temple treasury.
Finally, Leviticus 27:14-24 deals with the dedication of houses and fields. The concept of redeeming the dedicated house or field for its equivalent monetary value is the same as the examples already given. The laws of the Jubilee and their effect on land ownership are also discussed, although it doesn't change the behavior of the dedication.
To cross-validate what I have claimed above, consider the redemption of the first-born male child. Numbers 3:45-47 records G-d commanding Moses to take the Levites in place of the firstborn male children of Israel for service in the Tabernacle. Moses is also commanded to take five (silver) shekel coins for each of 237 people in excess of the Levites. The firstborn male children of Israel were originally supposed to serve as priests. But as Jewish tradition holds it, they forfeited this right to the Levites due to the sin with the Golden Calf in Exodus 32. As the firstborn males can no longer be holy to serve in the Temple, they must be redeemed for an appropriate value. And this practice actually continues to this day in Judaism.