In pirkei avot chapter 6 Rebbi Meir lists various benefits that will happen to one who learns "torah lishma" such as "it is revealed to him the secrets of the Torah. He becomes like an increasingly powerful river...It makes him great and exalted above all of creation.."
What is this torah lishma that Rebbi Meir is referring to?
Is it some kind of intent to have?
Like almost any good question in Judaism, there are a variety of opinions. I'll present a few here. In this case, though, I believe that the answers are not necessarily mutually exclusive: at the end of the day, everyone would agree to some extent that all of the following are noble motivations. As the Ben Ish Hai says in the beginning of Parshas Naso (2nd year), the one who learns "lishmah" has his heart directed towards Heaven.
To study Torah merely because it was a command may be the simplest understanding of "Torah Lishmah". This is indicated by the Gemara Sotah 22b and Rashi and Tosfos' commentary there. See Maharsha to Nedarim 62 where he states that the highest form of learning is that which is done "to fulfill the mitzvah, out of love for the one who gave the command". See below (third paragraph)
Learning for the purpose of knowing how to observe the mitzvos appears to me in my (admittedly limited) studies to be the opinion that appears to have the most support. One can bring support for this idea from the Gemara Berachos 17a, which states that the purpose of wisdom is תשובה ומעשים טובים, repentance and good deeds, and the Maharsha there assumes that this is referring to Torah wisdom as its being learned לשמה. Without being explicit, this is also indicated by the Yerushalmi there (Berachos 1:2, especially when compared with Kallah Rabasi 5:1) and the Sifra on the first verse in Bechukosai. Such a definition is assumed by Tosfos to Pesachim 50b and probably the Rosh there as well. This is also how the Tosfos Yom Tov explains the Mishnah in Avos 4:5 as well as the position of the Kesef Mishna (to Hil. Talmud Torah 3:10) and appears to be the opinion of the Vilna Gaon (tikkunei zohar vilna ed. pg 4). Another source is the Radak to Yirmiyahu 2:8
Studying Torah for the sake of better knowing or loving God is unquestionably a good thing. This appears to be the definition of the Meiri to Pesachim 50b who indicates that the only 'lishmah' is for the sake of the love of God. Similarly, the Baal HaTanya writes in Likutei Amarim ch. 5 that learning "lishmah" means for the sake of attaching one's soul to Hashem.
The Rambam has a similar understanding, in that he believes that true learning "lishmah", like all mitzvos (see intro to Perek Cheilek), is doing so with no ulterior motive whatsoever, but is done an expression of love of God (Hilchos Teshuvah 10:1, Commentary to Makkos 3:16)
Nefesh Hachayim (4:3) says that studying for the love of learning, to increase one's knowledge and discover the intellectual depth of the Torah is the highest goal of learning "lishmah". He bases this on a Rosh (to Nedarim 62a), and this is also clearly stated by the Ohr Hachayim to Bamidbar 24:6. This may not contradict the opinion of the Rambam, who besides for stating that learning should be done out of love of God, one should also do/study "what's true simply because it's true". Additionally, the son of the Rambam writes in a teshuvah (no. 82) that those who learn Torah lishma are those who do so "to find the truth".
The Alter Rebbe in Hilchos Talmud Torah (4:3) defines Lishma as learning LeShem Shamayim - for the sake of heaven. In other words, to do what G-d wants, and not to receive a reward in this world or the next, or because of fear of punishment in this world or the next. Certainly not to be a "Gadol" or any other such intention to use the Torah, or to win arguments, etc. He goes on there to elaborate that Lishma includes learning in order to keep and do Mitzvos properly.
That definition is most significant in its negative - it defines that all these other reasons that would not be lishma, leaving Torah study just because it is a Mitzvah as the Lishma. This is the Halachic definition of Lishma (according to the Alter Rebbe).
In Tanya, chapter 5 describes the Kabbalistic definition of Lishma as understanding Torah according to one's ability in order to connect his soul to G-d through that understanding. So learning Torah Lishma is then learning in order to be more of a G-dly person.
In Likkutei Torah (Shlach p. 47:3) the Alter Rebbe speaks of an even higher level in Torah Lishma, which is "for the sake of the Torah itself" to reveal G-d in the Torah above.
The Lubavitcher Rebbe (as summarized in the sefer ביאורים לפרקי אבות) explains that Pirkei Avos is about matters of piousness, above the letter of the law, but in this Braisa it is speaking about "All who learn Torah Lishma" thus this Braisa is about being Osek - working hard - in Torah for Torah's own sake, not for what he gets out of it in terms of knowing Halacha or in terms of his connection to Hashem, but not necessarily as high an appreciation as what it speaks of in Likkutei Torah.
The only reward he gets is the connection with G-d through Torah. But this leaves a person to wonder what will be with his service of G-d if he is absorbed in learning. The answer is the things listed in the Braisa - he becomes worthy and gains the ability to more easily earn the things listed in the Mishna. Some still require additional effort directed towards them (like things where it says מכשרתו להיות) but less effort, and others come automatically (those things which have to do with wordly matters), and others are part and parcel of the effort in learning, such as being revealed the secrets of the Torah.
So in other words, the point of the Braysa is that by learning Torah Lishma, Hashem makes other matters easier or just takes care of them automatically, leaving one free to focus on learning.
Torah L'shma is learning Torah for the sake of learning torah, to learn the Truth. And not, in contrast, to learning Torah in order to be exalted above creation, or to become like a powerful river, or in order to have all the secrets revealed. ;)
The irony is lost on many.
Lishma means for its own sake. As in, the motivation to do a certain thing is that you do it, not certain benefits (like favor with G-d) that may come with completing the task.
For the experience of learning Torah itself, without any external motivation.
This was described in detail by Ba'al haSulam and recorded by the Rabash in Shamati article 5, called "Lishma".
Original: https://kabbalahmedia.info/he/sources/1onNjaw2
English translation: http://www.kabbalah.info/eng/content/view/frame/31769
