We begin with chapter 11 of Maseches Terumos, mishnah 4. The subject of the mishnah is the stems of fruits. It is worth noting that an entire tractate is devoted to this topic - Maseches Uktzin - which shows that there is a great deal here to discuss.
The Basic Question:
The question the mishnah addresses is whether the stems have the status of Terumah just as the fruit itself does. Almost all fruit stems are not fit for eating at all, since they are nothing but wood - part of the tree - and are certainly not food or fruit. And just as the tree itself does not have the status of Terumah, but only the fruit, which is the part fit for eating, so too the stems, which are merely inedible wood, do not have the status of Terumah.
However, there are stems that lie on the borderline of being edible: people generally do not eat them, but someone who wishes to eat them can. The most prominent and familiar example is the stem of figs; on a dried fig, for instance, people are not accustomed to eat the tip of the stem, but it can be done. What, then, is the law regarding these stems?
The Words of the Mishnah:
"Uktzei te'einim u'grogaros v'hakelisin v'hecharuvin shel Terumah - asurin l'zarim" - the stems of figs, dried figs, kelisin and carobs that are Terumah are forbidden to non-kohanim.
"Uktzei te'einim" - the stems attached to figs, those stems that lie on the borderline of being edible.
"U'grogaros" - dried figs.
"V'hakelisin" - another variety of fig, or a different type of fruit.
"V'hecharuvin" - carobs, known to us also as 'bokser'. They have a good taste when they are eaten fresh.
"Shel Terumah - asurin l'zarim" - when the carob or the fig is Terumah, the stem remains forbidden to anyone who is not a kohen. In other words, these stems do have the status of Terumah, and a non-kohen may not eat them.
In summary: We have learned that stems which are nothing but inedible wood do not have the status of Terumah, just like the tree itself. But the stems listed in the mishnah - those of figs, dried figs, kelisin and carobs - lie on the borderline of being edible, and therefore they do have the status of Terumah and are forbidden to non-kohanim.