In his introductory comments on the Talmudic tractate Megillah, the Ramban explains that the idea behind sending the books near and far means that they were sent through the entire expanse – from Hodu to Cush (Esther 1:1) – of Achashverosh’s kingdom.
Me’am Loez suggests that they were even sent to other countries.
The Dena Pishra explains that since Mordechai’s goal was to create a feeling of achdus (“unity”), he even wanted to reach those Jews whose lack of faith and subsequent fear motivated them to flea battle.
Rav Schwab, however, understands “close” as those Jews who were living in Shushan and celebrating on the 14th of Adar, whereas “far” refers to those Jews who returned to Eretz Yisroel and celebrated Shushan Purim on the 15th of Adar in the only place where one must certainly do so – the holy city of Yerushalayim.
The Sha’ar Yissachar writes that the books were sent near and far so no Jew could ever devise the excuse that they are too far from holiness. Rather, the near and far have equal access to the holiness that emanates from Purim.
Keser Shem Tov quotes that Talmudic (Megillah 17a) rule that Megillas Esther on Purim must be read as written, and not backwards. The Keser Shem Tov then wonders why anybody would think to read it backwards. He posits that the Talmud means that nobody should ever consider the Purim story as some ancient, historic event without real relevance to our lives.