Before us is Mishnah 8 in the third chapter of Maseches Avodah Zarah, which likewise deals with the prohibition of deriving benefit from an asheirah - a tree of idolatry. Three situations fall under the definition of an asheirah:
A tree beneath which an idol is currently placed.
A tree that was worshipped in the past.
A tree that was planted from the outset for the sake of idolatry, so that it would be worshipped in the future.
In each of these situations the tree is forbidden to derive benefit from, and from this the laws of our Mishnah follow.
"Lo yeisheiv b'tzilah":
One may not sit in the shade cast by the tree, and this applies even when a person is not directly beneath the branches: when the sun is low on the horizon and the tree casts a long shadow, it is forbidden to sit even at a distance from the tree, since sitting in its shade is benefit derived from a tree that is forbidden to benefit from.
"V'im yashav - tahor" - even though he transgressed the prohibition, he does not become tamei, since he sat only in the shade and not literally beneath the branches.
Why would we have thought that he would become tamei?
The Mishnah assumes that beneath the tree there are offerings lying on the ground that were brought earlier to the idol, even in the amount of a k'zayis. Our Mishnah follows the view of Rabbi Yehudah ben Beseira, who holds that these offerings convey tumah not only through touching and carrying - which is the accepted halachah - but even through ohel, that is, when a person is above them, beneath them, or under one roof together with them.
Therefore one who stands directly beneath the branch becomes tamei with tumas ohel; but one who sits at a distance from the tree, merely in its shade, is not reached by the tumah and remains tahor.
"V'lo ya'avor tachteha":
It is forbidden to pass beneath the tree, and this prohibition is not because of tumah but because of the impression created: one who passes beneath the tree looks as though he wishes to derive benefit from it, and a person is obligated to distance himself from idolatry and not to appear as someone receiving benefit from it.
"V'im avar - tamei" - according to Rabbi Yehudah ben Beseira, we assume that offerings are lying on the ground beneath the branch, and those offerings convey tumah like a corpse: one who is together with them under one roof is like one who is under one roof with a k'zayis of a corpse. The basis for this is the name the verse gave them - "zivchei meisim" (sacrifices of the dead) - and in the view of nearly all the commentators this is only an asmachta: we relate to them as a corpse, and for that reason they convey tumah through ohel. According to Rabbeinu Tam, one who walks beneath that branch is tamei out of doubt, and since this doubtful tumah is rabbinic, he treats himself as tamei.
"Haysah gozeles es harabim":
The simple meaning is that the tree is robbing the public. The case is one where there was a public path, and afterwards a branch of a tree of avodah zarah came to jut out over it - whether the tree grew and spread its branches over the path, or a branch was already jutting out there and someone came and made the tree into an asherah. A person has no right to rob from the public, and therefore the public is not restricted in its passage.
"V'avar tachteha - tahor" - one who passes beneath a branch jutting out over a public domain remains tahor. For even according to Rabbeinu Tam, the tumah here is only rabbinic, since there is no direct, certain knowledge that an offering is placed there, and even the tumah itself rests only on an asmachta - therefore the Sages did not decree tumah in a case of "robbing the public," where the public thoroughfare passes beneath the area into which the tree has spread.
It is worth noting that in practice, if a person has another option, he should avoid the road that passes beneath the tree, so that he not appear to be seeking to derive benefit from it.
Sowing beneath the tree:
The rule here is straightforward: if the one who sows receives no benefit from the tree - it is permitted; and if he does benefit from it - it is forbidden.
"Zor'in tachteha yerakos bimos hageshamim" - in the winter season the one who sows wants as much sunlight as possible, and the tree does him no good at all: it casts shade and it even prevents the rain from reaching the vegetables. It turns out that there is no benefit here, and there is not even any impression of benefit, since everyone can see that he gains nothing - and therefore it is permitted.
"Aval lo bimos hachamah" - in the summer season the shade cast by the tree protects the vegetables and helps them grow, so the one who sows is benefiting from the tree - and it is forbidden.
"V'hachazarin lo bimos hachamah v'lo bimos hageshamim" - chazeres is Romaine lettuce, and sunlight is not good for it at all; rather, any reduction of sunlight helps it grow. Even in the rainy season, when the sun comes out, the shade assists it, so the one who sows benefits from the tree in every season of the year - and therefore it is always forbidden to sow it beneath the tree.
The dispute between Rabbi Yosi and the Sages:
To understand the dispute, one must recall Rabbi Yosi's position, which was already taught several mishnayos earlier: "zeh v'zeh gorem" is permitted. That is, when two factors contribute to a single thing, one of them forbidden in benefit and the other permitted - the end product is permitted in benefit. The first case in which this was taught was the permission to grind up an idol and scatter its dust to the wind: even if the dust forms a layer of soil and plants grow in it, zeh v'zeh gorem - forbidden soil and permitted soil combine, and the result is permitted. The Sages, however, hold that "zeh v'zeh gorem," at least in matters of avodah zarah, is forbidden: if even part of the contribution to the growth comes from something forbidden in benefit on account of avodah zarah, the product is forbidden.
Rabbi Yosi therefore argues: according to my position it is permitted to sow vegetables beneath the asherah both in summer and in winter, since the shade alone does not grow the vegetables, but rather zeh v'zeh gorem. But according to your position, Sages, that any benefit from the tree forbids what grows beneath it, the ruling does not hold together.
"Rabbi Yosi omer: af lo yerakos bimos hageshamim, mipnei shehanemiyah nosheres aleihen v'havya lahen l'zevel" - the leaves of the tree fall in the autumn, and those leaves become like fertilizer that enriches the ground and helps the vegetable grow. It turns out that even in winter the vegetables grow in fertilized ground, and the fertilizer comes from a tree that is forbidden in benefit - here you have zeh v'zeh gorem, which according to the Sages is forbidden. How, then, can they permit sowing even in the rainy season?
The Sages, however, do not accept this reasoning. True, there is a certain amount of fertilization from the fallen leaves, but it is nullified by the majority: whatever good it does is offset by the rain the tree blocks and the sun it blocks, neither of which is good for winter sowing. In the final analysis, one who sows beneath the tree is worse off than one who sows away from it, and there is no benefit at all in such sowing - and therefore it is permitted according to the Sages.
The halachah: The ruling is that 'zeh vazeh gorem' (a result produced by both a permitted factor and a forbidden one) is permitted, and therefore one may sow beneath an asheirah tree both in the summer months and in the rainy season.