The word "tevul yom" refers to a person who has immersed in a mikveh but will not become pure until the evening. The concept is derived by the rabbis from the following two verses:
Leviticus 11:32 And anything on which one of them falls when dead shall be unclean: be it any article of wood, or a cloth, or a skin, or a sack — any such article that can be put to use shall be dipped in water, and it shall remain unclean until evening; then it shall be clean.
Leviticus 22:6-7 6 The person who touches such shall be unclean until evening and shall not eat of the sacred donations unless he has washed his body in water. 7 As soon as the sun sets, he shall be clean; and afterward he may eat of the sacred donations, for they are his food. 8 He shall not eat anything that died or was torn by beasts, thereby becoming unclean: I am the Lord.
According to rabbinic law, a kohen goes to the mikveh before the sun sets but cannot eat terumah until after the sun has set. This is the meaning of Leviticus 22:7. So too a vessel which has become impure through a sheretz (a creepy crawly thing) is immersed in a mikveh and then can be used with terumah in the evening, when the sun has set. Until the sun has set, both the person and the vessel are called a "tevul yom."
A "tevul yom" is not actually impure. Once he or the vessel has been in the mikveh, he or the vessel is pure. If a tevul yom touches terumah he disqualifies the terumah from being eaten, but it is not impure. Indeed, there is a special leniency with terumah that has been disqualified because it was touched by a tevul yom. Generally, disqualified terumah will disqualify sacred food it touches. But in this case, the terumah does not disqualify sacred food.
This tractate is highly technical, dealing with the nitty-gritties of impurity law. But by now, those of you who have been following along are real experts in these laws, so it shouldn't be difficult at all ☺.