The “taxes” paid by your average farmer during Temple times went largely to the mikdash itself and to the people – kohanim and levi’im – who worked there. The major matanot (literally “presents” but effectively taxes) included:
Teruma gedola – a portion of the harvest given to the kohen. He can use it in his home for normal purposes, but it must be treated as kodshim, preserved (when possibly in a state of ritual purity, only consumed by kohanim, etc.)
Ma’aser sheni – a portion of the harvest that is taken by its owner to Jerusalem, where he can eat it on his own or give it to others, but it must be kept tahor and only eaten within the precincts of the city.
Our Gemara quotes a Mishna that teaches a number of halakhot regarding bikkurim and teruma. For example, someone who is not a kohen who eats them will be liable to receive the death penalty if he consumes them with malicious intent, or will have to pay restitution and add a 20% penalty if he eats them accidentally. Nevertheless, they are considered the property of the kohen (i.e. he can sell them to another kohen), and if they were to fall into a mixture, they would become nullified at a ratio of 100:1 (ordinary forbidden foods become nullified at a ratio of 60:1). The Mishna points out that all this is in contrast to the laws of ma’aser rishon, which has no unique holiness to it; it is simply a portion of the harvest that must be separated and given to the levi to do with it as he sees fit.
The Ramban points out that the emphasis of the Mishna on the fact that bikkurim and teruma are the property of the kohen is to point out the contrast with ma’aser sheni which is considered by the Sages to be in the category of mi-shulhan gavoah ka-zakhu – that it comes to the individual “from the table of the Almighty.”