The International Standard Bible Encyclopedia (vol. 4, p. 863) lists three tithes. It is amazing to see how many commentaries and dictionaries list the same three tithes with regard to Leviticus 27:30-34 and Deuteronomy 14:22-29:
Jewish tradition and some more recent studies (e.g., Landrell, p. 36) have identified two or three different tithes in these passages. (1) A first tithe consisted of the tithe to the Levites. . .; of this, one tenth was passed on to the priest or to the house of God. (2) A second tithe (from the remaining nine tenths) was set apart and eaten by the household, presumably in Jerusalem (Deuteronomy 14:22-26 . . .). Those living far from Jerusalem could change the tithe of the land into money . . . [for] food, drink, or oil. . . . Landsell refers to this tithe as the tithe for the sacred celebration. [This is exactly what it is—the tithe for the sacred celebration!] (3) The third tithe, according to Jewish tradition (Josephus, Antiquities of the Jews iv.8.22 [240-243]; cf. also Landsell) was the tithe for the poor (Deuteronomy 14:28f), which occurred only in the third year. According to some of these possible scenarios, the tithing rate could run as high as thirty percent! (Emphasis added.)
Eerdmans Family Encyclopedia of the Bible (p. 147), under "Tithing":
Each year a tithe (a tenth of one's produce) was given to God for the upkeep of the priests. A second [tithe] was used for a sacrificial meal, in which the worshipper and his family shared at one of the festivals. A third [tithe] was used to help the poor.
The International Standard Bible Encyclopedia (ibid.), under "Tithing: Theological Implications":
No institution in Israel, including tithing, existed merely to carry out a political, economic, or humanitarian function. By giving the tithe, the Israelites were declaring solemnly that they were giving a portion back to the Lord who had prospered them (Deuteronomy 26:10-15). By giving the tithe they also recognized the validity of the priests' and Levites' role as God's representatives and acknowledged their right to receive support for the spiritual service they performed on the people's behalf. The tithe ritual afforded the Israelites an opportunity to remember Yahweh's blessings as He had remembered them, and to imitate their God's care for slaves, the poor, orphans, and widows. The tithe demanded that the Israelites serve their God at a significant cost to themselves. In this amazing system of tithing, Israel's economics became a channel for expressing love to God and love to neighbors the heart of the Torah (Deuteronomy 6:4-9; Leviticus 19:18).
What are the greatest commandments of the law in Matthew 22:36-40? They are to love the Lord your God with all your heart and to love your neighbor as yourself. Jesus says that on these two commandments hang all the law and the prophets. This is what God's tithing law is to do.
The International Standard Bible Encyclopedia adds: "[T]ithing helped to set Israel apart as Yahweh's people and His alone, a people holy to Him." This is because of their obedience to God. Of course, we know that other signs identifying God's people are keeping God's Sabbath, obeying the laws of clean and unclean meats, keeping the holy days—these are, along with simply obeying God in all He tells us to do, true signs of God's people.