I heard an explanation from Rav Yisraeli shlita (I subsequently found the same idea in some seforim.) The Gemorah in Sanhedrin (99b) says שנאמר (משלי טז, כו) נפש עמל עמלה לו כי אכף עליו פיהו הוא עמל במקום זה ותורתו עומלת לו במקום אחר. Rashi says (girsah of Eyen Yaakov,) שמחזרת עליו ומבקשת מאת קונה למסור לו טעמי תורה וסתריה. We see that the Torah itself prays to Hashem for a person to be successful in their learning. How can the Torah beseech Hashem for a person? Because the Torah is Torah Chayim. As I like to tell my sister when she says quiet, only dead things are quiet. Learning Torah is not studying some ancient, dead history. Torah is a living screaming organism. By assuring הדרן עלך, that you have not left the Tractate behind, it will be הדרך עלן, it will help you understand the next Tractate as well.
The Haghos Ashri end of Sukkah brings the midrash (Shir Hashirim 1:9 ) that says after Shlomo asked Hashe for a לב שומע, wisdom and understanding, מיד ויבא ירושלים ויעמוד לפני ארון ברית ה' ויעל עולות ויעש שלמים ויעש משתה לכל עבדיו, א"ר אלעזר מכאן שעושין סעוד' לגמרה של תורה. How is this a source for making a siyum, Shlomo did not learn anything yet, he was just given greater ability? We see the celebration is for the Torah that was learnt, rather it is for the Torah that will be learnt. In other words, after one finishes a Tractate, their connection to Torah is strengthened. The Torah will come to the individual's aid to be able to have a greater understanding in Torah. That is the הדרן עלן, celebrating the greater insights in Torah that are possible because one has finished a Tractate.
Many come into Simchas Torah wondering what is the simcha for me, I didn't learn enough this year, I'm not learning in yeshiva/kollel, what does it have to do with me? The answer is that we are not celebrating last year's learning, it is a time of commitment for the future. In some institutions people make learning pledges for the upcoming year. That is taking upon themselves the commitment for the future (Kotzker.)
On Sukkot there are the great celebrations of the בית השואבה. Why is the simcha called the simcha of the בית השואבה, when the mitzvah is not the drawing of the water, rather the libation? And what is so great about the water libation that it deserves such simcha? Rashi Vayikra (2:13) tells us since the water that was placed on earth complained that they were being sent further away from Hashem they meir to be offered in the water libation on Sukkot. The water libation indicates our desire to do more, to come closer to Hashem. That is what we are celebrating. That is why the celebration is for the בית השואבה, for we are not celebrating the completing of the mitvah, rather the opportunity to reconnect ourselves to Hashem. That starts with the preparation of the mitzvah. It is the new opportunity of having shed our baggage of the previous year on the High Holy days and now we are starting a better relationship with Hashem (see the Hornosteipel.)