Taharos, Chapter 2, Mishnah 3. Here the Mishnah looks at one specific type of food: chullin that was produced under the purity requirements that apply to terumah. Certain individuals were careful to treat even their everyday, non sacred food with the sanctity and cleanness demanded of terumah, and once they did, that food takes on grades of tumah that ordinary chullin never has. Our mishnah goes through those grades in order, spelling out the power of each one and where that power ends.
The rishon
"Harishon shebechullin, tamei umetamei." The first level in this chullin is both tamei itself and capable of conveying tumah onward. Whatever it touches becomes tamei in turn, and that item can continue to pass tumah along. This is full, active tumah.
The sheini
"Hasheini posel velo metamei." The second level is more restricted. It does have an effect on what it touches, rendering it a shlishi, which means that the food it touches becomes pasul, unfit for consumption. But the chain stops there. A shlishi has no power to do anything to terumah, so the item the sheini touched cannot pass its disqualification any further. The sheini disqualifies but does not transmit tumah.
The shlishi
"Vehashlishi ne'echal binzid hadema." A shlishi is permitted even when it enters cooked terumah. Dema is the Mishnah's word for terumah, so the situation before us is chullin that has reached the third grade and then lands in a pot of terumah porridge. Because a shlishi retains too little tumah to affect anything it meets, nothing in the pot is harmed, and the combined food remains permitted for eating.
Elsewhere Chazal attached a precise limitation to this allowance. The amount of such chullin has to be smaller than a kezayis consumed within the interval called kedei achilas pras, the span of time required to eat a pras of bread. The picture, then, is not of a real quantity of food stirred into the pot, but of something functioning more like flavoring: a spice or minor ingredient holding the status of shlishi that gets added to terumah that is cooking.
Read together, the three clauses give a clear picture of how tumah weakens as it travels through chullin that was made on the level of taharas terumah: full transmission at the first stage, disqualification without transmission at the second, and at the third a status so faint that the food may still be eaten alongside terumah itself.