Sukkah, Chapter 3, Mishnah 3. We continue with the same topic that the previous two mishnayos dealt with: which features of each of the four species are valid and which are invalid. This mishnah deals with the aravah (willow).
The invalid willows:
The mishnah opens: "aravah gezulah viyeveishah - pesulah" - a stolen or dried out willow is invalid.
"gezulah" - a stolen willow is invalid for one of two reasons: because it must belong to the person himself, or because this is a mitzvah that comes about through a transgression.
"yeveishah" - a willow that has dried out is invalid because of "hadar" (beauty), since it no longer has its natural beauty.
"shel asheirah v'shel ir hanidachas - pesulah" - one from an asheirah tree or from a condemned city is invalid:
This refers to a willow that comes from a tree that was worshipped as idolatry, or from a city whose inhabitants worshipped idolatry, in which case all of its items must be burned, and likewise an asheirah must be burned. Since the halachah is that it must be burned, we view it as though it has already been burned, and so it lacks the shiur, the measurement required for it to be valid.
The mishnah continues: "niktam rosha, nifretzu alehah, v'hatzaftzafah - pesulah" - one whose top was broken off, whose leaves were stripped away, and the tzaftzafah, are invalid.
"niktam rosha" - the top of the willow was broken off.
"nifretzu alehah" - the leaves were torn off it.
"v'hatzaftzafah" - a type of willow whose leaves are rounded, with serrated edges, and whose stem is white. All of these are invalid.
The valid willows:
In contrast, the mishnah rules: "kemushah, v'shenashru miktzas alehah, v'shel ba'al - kesheirah" - one that is withered, one from which some of its leaves fell off, and one grown by rainfall, are valid.
"kemushah" - a willow that has withered.
"v'shenashru miktzas alehah" - only some of the leaves fell off, but most of the leaves are still attached.
"v'shel ba'al" - a willow that did not grow beside a stream but rather in a field, sustained by rainwater alone, and was not nourished by a stream. The Torah describes the willow with the expression "arvei nachal" (willows of the brook), meaning willows that grow beside a stream, and that is indeed what is common and usual, but it is not a requirement.
In summary: these three cases - a withered willow, a willow missing some of its leaves but where most still remain, and a willow that grew in a field on rainwater - are all valid.