As the Torah tells us (see Shemot 30:11-16) every Jewish adult male was commanded to bring a mahatzit ha-shekel – a half-shekel – as a donation to the Temple service. It is clear from stories in Tanakh that this obligation was not just for use in the mishkan in the desert, but was an on-going requirement for as long as the Temple stood. The story of the re-dedication of the Temple by King Yeho’ash – and his specific request that the mahatzit ha-shekel be brought – appears both in Sefer Melakhim (II Melakhim 12:5-6, where it is called kesef over, a reference to the person who is over al ha-pekudim, see Shemot 30:13) and in Divrei ha-Yamim (II Divrei ha-Yamim 24:9-14, where it is referred to as mas’at Moshe – Moshe’s tax).
We also find this commandment mentioned during the Second Temple period. In Sefer Nehemiah (10:33-34) we learn that the yearly tax was one-third of a shekel, whose purpose was to pay for the communal sacrifices.
The value of a shekel varied with time, and in every generation it was necessary to figure out the exchange rate so that the value of a half shekel would be given in the currency of that time. According to the Ramban, the Persian money was worth more so the value of one-third of a shekel was the equivalent of the half-shekel of the Torah. During the time of the Mishna the shekel was worth half of a sela, so that one Mishnaic shekel was the equivalent of the Biblical half-shekel, which is why we will find the Mishna referring to a shekel when discussing this mitzva.
Mishna: On the first of Adar the court proclaims concerning the collection of shekels…
Gemara: And why specifically on the first of Adar? The Gemara answers: This was done in order that Jews would bring their shekels to the designated Temple chamber in the proper time, as the shekels had to be collected before the beginning of Nisan each year. And this would ensure that the collection of the Temple treasury chamber would be collected from the new shekels at its proper time, which is on the first of the month of Nisan, i.e., the beginning of the Temple year. After that date all communal offerings must be purchased from the new shekels.