Imagine if every few years the Gregorian calendar had two Decembers. When would people shop? We of course are faced with a similar dilemma seven out of every nineteen years, as our calendar has two Adars. While we celebrate Purim in Adar II, this was actually the subject of rabbinic debate.
The Talmud instinctively understood that we should celebrate Purim in Adar I; we should never pass up an opportunity to perform a mitzvah. Furthermore, is not the first Adar the real Adar, with the second added to balance our lunar and solar calendars? In fact, the court could wait until the 29th day of Adar (it is Nissan, not Tishrei, that marks the beginning of the calendar year) to decide if it was even necessary to add an extra month. Clearly, one would have to have read the megillah two weeks earlier, in the middle of Adar I. Yet the Talmud accepts the reasoning that Purim should be celebrated in Adar II based on the desire to have “redemption next to redemption”, i.e., that we should celebrate the miracle of Purim as close as possible to the celebration of the miracle of Pesach. 
This connection between these two seemingly unrelated holidays appears in many sources. Rashi explains that the reason that “when Adar enters we increase our joy” is due to our recall of the miracles of Purim and Pesach. The first law codified in the laws of Pesach is that we should start learning them thirty days prior, i.e., on Purim itself. The key elements of the Purim story took place at Pesach - the three-day fast coincided with what should have been the seder. 
Yet the connection between Purim and Pesach requires further elucidation. Why are we so insistent on placing Purim next to Pesach? The redemption of Pesach and the redemption of Purim could not be more different. On Pesach, G-d actively intervened to change the course of history. The Jewish people are (almost) completely passive throughout the whole process, relying on the overt miracles of G-d to redeem them. The role of the Jewish people is so insignificant that at our seder, which celebrates our first redemption, the name of Moshe is not even mentioned. It is as if our great leader played no part in the Exodus. 
On Purim, we find exactly the opposite situation. There are no overt miracles, the central roles are played by Mordechai and Esther, and the role of G-d is so “behind the scenes” that His name is nowhere to be found in the Megillah.
Pesach celebrates the formation of the Jewish nation. A group of slaves who were far removed from G-d had to be taught that G-d is the Master of the Universe. Maimonides begins his monumental code of Jewish law declaring that, “the foundation of foundations and pillar of wisdom is to know that there is a G-d”, Who is the source and cause of all of existence. Pesach is the holiday on which we celebrate G-d’s role in history.
A thousand years later, we are able to recognize G-d even when He is hidden. Purim, in effect, represents the maturation of the Jewish people. No miracles are needed, as we understand that all that transpires is the will of G-d. Our calendar symbolically reflects this growth process. At the beginning of the year, in Nisan, we are in essence little children, who have difficulty understanding abstract concepts and need to see the direct power of G-d to be impressed. By the end of the year, in Adar, we have grown into adults, with a more sophisticated approach to our Master. Purim and Pesach cannot be separated; the link between open and hidden miracles must be emphasized.
Our Sages tell us that the story of Esther marks the end of the period of miracles. Once one understands that all of existence is a miracle, that Esther was the agent of G-d in redeeming the Jewish people, no more miracles are necessary. 
We can now begin to understand why our Sages place such emphasis on Purim, equating it in importance to that of Yom Kippur. They saw it as a day of rededication to Torah, (recall the Torah we have today was given on Yom Kippur) and suggested that, while the books of the Neviim and Ketuvim will someday be abrogated, the book of Esther will never be annulled from the canon. 
While we are full of joy as we recount the miracles of Pesach, a higher form of joy is to be found in the miracles of Purim. MiShenichnas Adar Marbim BeSimcha, when Adar enters we increase our joy. May we merit the ultimate joy of the final redemption. Shabbat Shalom!