There is a commandment to remember 'Amaleq and to read the portion of Zakhor (remember) from the Sefer Torah. There is no specfic time connected with this commandment, so why do we read it specifically on the Shabbath before Purim?
It says in the Gemarra of Meghilla that Zakhor is read before Purim because we wish to mention the eradication of 'Amaleq alongside the eradication of Haman, as it says in the Meghilla: "And these days shall be remembered and celebrated". "Remember" (which is mentioned first) refers to reading Zakhor, and "celebrate" refers to the eradication of 'Amaleq. That is why Zakhor (remember) is read on the preceding Shabbath.
In addition, every miracle that occurs sees a re-awakening every year. That is why all the Holidays (Pesah, Purim and so on) come around every year. This re-awakening always starts from the Shabbath before the Holiday. From the Shabbath before Purim there is a re-awakening of the actions that caused the repentance and the Geullah (redemption).
The Shabbath before Purim sees an amazing (spiritual) light that assists Israel. That is why the Jewish people must engage in the study of the Torah on that Shabbath, more than any other Shabbath, to awaken the redemption and the elevation of Qedusha (holiness) that arises on this day.
(Meghilla 29a with Rashi. M.M 685: 1. Dabar Be'Itto, Derush on Zachor/Purim)
