"Machatzit Hashekel" means a half of a Shekel. When the Holy Temple stood in Jerusalem, every Jewish man over the age of twenty (according to other Halachic authorities, from the age of thirteen) was annually required to donate half a silver Shekel to the Temple coffers. “Shekel” is the name of the currency which circulated in Israel during Biblical times. [In fact, the Shekel is also the name of the modern-day Israeli currency.] A half Shekel was approximately 10 grams of silver.
The Half Shekels were primarily used to purchase cattle for the communal sacrifices which were offered daily, as well as the additional sacrifices offered on Shabbat and holidays. The leftover funds were used for a variety of communal purposes, including providing salaries for the judges and maintenance of the Temple, its vessels, and the city walls. This annual tax was due on the 1st of Nissan. One month earlier, on the 1st of Adar, The courts would begin posting reminders about this Biblical obligation. We commemorate this Biblical law by giving a Machatzit Hashekel to charity.
Before Minchah of the Fast of Esther we give to charity a coin which is half of the local currency. In the USA this means giving a half-dollar coin. Don’t sweat if you don’t possess such a coin—at the Minchah service most synagogues provide such coins to their congregants at price. It is actually customary to give three half-dollars for every member of the family. This commemorates the three contributions the Jews gave for the building of the Tabernacle and its sacrifices (see Rashi's commentary on Exodus 25:2).
See also Why do we give the Machatzit Hashekel to charity on the Fast of Esther?
We also commemorate this Mitzvah on the Shabbat directly preceding the month of Adar by reading the portion in the Torah which speaks of this commandment.1 On this Shabbat, known as "Parshat Shekalim," we take out of the ark a second Torah and from it we read the section dealing with the Half Shekel.