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.