Chazal (Shabbos 21:) say, בהלל קבעום האחרת לשנה והודאה, that the chachamim established Chanukah as a holiday "on the following year." Why did they wait a year to establish Chanukah instead of establishing the yom tov on the year that it happened? The Kedushas Levi (Kedushah Rishonah, see also Ben Yehoyada) explains that initially they thought that the miracles of Chanukah were a one-time matter, a miracle to save the Yidden then. The following year, the chachamim perceived that the miracles were recurring. They understood that the miracles of Chanukah would happen yearly, so they established Chanukah as a holiday to be celebrated again and again.
The chachamim saw how the Yidden improved their ways, and lived more spiritually than before, causing more miracles and chesed to descend to the world. When the chachamim understood how Chanukah changed the Jewish nation for the better, they established it as an annual holiday.
The simple meaning of this Chazal is that, on Chanukah, it is forbidden to use a clay lamp (חרס כלי) that has already been used in the past. This is because once it is used, it loses its beauty; it turns black and ugly, and it is a מצוה בזוי, a disgrace to use for a mitzvah. However, the Bnei Yissaschar explains that this reason isn't sufficient because if it is a מצוה בזוי, it would be forbidden to use such a lamp on Shabbos and yom tov, as well. Instead, Chazal are hinting at another lesson, related specifically to Chanukah, and that is that we aren't focusing only on the miracles of the past, ישן נר. Instead, we celebrate the miracles that occur each year.
The Gemara (Shabbos 23.) states, "When one lights Chanukah lecht, he must make a brachah. מברך מאי, What brachah should he say? חנוכה נר להדליק וצונו במצותיו קדשנו אשר ...'ה אתה ברוך, "Bless are You Hashem... Who sanctified us with His mitzvos and commanded us to light Chanukah lecht." The Gemara asks, צוונו היכן, "When did Hashem command us to light Chanukah lecht?" [Chanukah is a yom tov instituted by the chachamim!] The Gemara replies (Devarim 32:7), ויגדך אביך שאל, "Ask your father and he will tell you..." Hashem commands us to obey our chachamim. (The chachamim commanded us to light Chanukah lecht, and Hashem obligated us to listen to them, so it is as if Hashem commanded us to light Chanukah lecht.)
Rebbe Yisrael of Tchortkov zt'l explains the Gemara b'derech remez: The Gemara begins, "When one lights Chanukah lecht, he must make a ברכה." A בריכה or הרכבה can also be translated as grafting, when you merge two plants to grow as one. The Gemara is saying that when one lights Chanukah lecht, he must say a ברכה. This means he must create a connection from the source of miracles to the Jewish nation. This is because the miracles of Chanukah repeat themselves each year, and Klal Yisrael can receive many yeshuos and salvations, but we must make the connection. We have to create a הרכבה between the source of salvation, so that they should come down to the entire Jewish nation. The Gemara asks, מברך מאי, "How does one make this connection?" The Gemara replies וצונו, that we should become connected with Hashem. (The word צוונו can mean connect, as in the word צוותא).
The Bnei Yissaschar (Kislev 4:9) teaches that the miracles of Chanukah happen again each year. We aren't only commemorating a miracle that occurred in ancient times, millenniums ago. This is hinted in the Chazal (Masechta Sofrim 2:1), which says ישן בנר להדליק אסור, "It is forbidden to light Chanukah lecht in an old lamp." We aren't only remembering the miracles of olden times but rather the nissim that occur now.
About Purim
Chazal (Megillah 17.) say, הקורא יצא לא למפרע מגילה. The Bnei Yissaschar repeats from his Rebbes, למפרע מגילה הקורא, if one reads the megillah like it was an episode that happened in the past, יצא לא, he didn't perform the mitzvah correctly. This is because the miracles of Purim aren't only about something that happened in the past. Every generation has its Haman (or Hamans) who want to destroy us, r'l, and each year, Hashem saves us anew, in the merit of the mitzvah of reading Megillas Esther and all the other mitzvos we perform on Purim. The Bnei Yissaschar says that something similar occurs with the Chanukah lecht. When we light Chanukah lecht, the miracles recur. Thus, Chazal say, ישן בנר להדליק אסור, "It is forbidden to light in an old lamp." It isn't an "old lamp". It is yeshuos that are happening to us today.
The Gemara continues, צוונו היכן, how does one connect with Hashem? The answer is ויגדך אביך שאל, ask the tzaddikim and follow in their ways. Emulate their good deeds. Do as they do, and you will be connected to Hashem, thereby drawing down the blessings and salvation of Chanukah.