Just for a example of this first level. Pesachim 29b
In the Talmud there is an argument what happens if one eats leavened bread that belongs to the Temple on Passover. Is he required to bring a sacrifice? This is a debate. Rav Ashi says the reason for the one who says one must bring a sacrifice is because he hold one can derive pleasure from leavened bread on Passover.[That is everyone, not just the Temple.] [So he was נהנה (had pleasure) from הקדש (something that belonged to the Temple) so he brings a sacrifice]
Rav Ashi says that everyone is agreeing that one can't redeem the leavened bread on Passover. But the reason one brings the sacrifice is that since the leaven only has holiness of monetary value, it can be used to lite one's stove. That is the first level of Tosphot which seems to not make sense. Leaven seems more like holiness of body that can't be redeemed.
The next level is to understand that to the Temple, the leaven does have monetary value. So it makes sense to say it has holiness that applies to monetary value on Passover itself. We do not find that even on Passover that the Temple can't derive benefit from leaven. So it makes sense to say the Temple can sell it to be used to lite ones stove.