The Sabbath closest to the Purim holiday is called Shabbat Zachor because of the maftir (Torah reading that follows the portion of the week, usually a repetition of the last part of the reading) which is a special one that is not part of the regular Torah portion.
Zachor means "remember!" The Torah commands the Jews to remember how the tribe of Amalek attacked them from the rear whle they were in the desert, weak and just freed from slavery. Amalek attacked the sick and elderly who travelled more slowly than the rest. A battle led by Joshua defeated them, with the help of G-d - in fact, the Bible says that when Moses lifted up his hands to the heavens, the tide turned in favor of the Israelite warriors and they defeated the Amalekites.
G-d told the Jews never to forget this cowardly treachery and to make sure to destroy the people of Amalek in every generation. This was not accomplished, for various reasons, and Haman the Aggagite was a descendant of Agag, king of Amalek in King Saul's reign. This is why the portion is read close to Purim.
It is a Torah commandment to attend the synagogue and hear the reading of this portion. It is read while the congregation rises and is often read several times, in the varied accents of the congregants, so that every word will be clearly understood. Many congrefations have a second reading for mothers who cannot leave their young children and await the father's return from prayer to be able to hear Parshat Zachor.