There are 3 aspects of shekalim, each related to historical events in respect of mentions of the shekel in tanach and talmud
1. Torah (Vayakhel-Pekudei): COUNTING and BUILDING and ARMY. (Approx 2200BCE) Moshe after matan torah makes the mishkan - the purpose is to count the people with half-shekels and then take the silver obtained and melt it down into the adanim sockets for the mishkan. This is like the sephardim who contribute parts of the shul and put their name to it.
2. Tanach (Kings 2, ch11-12): RENOVATION. (Approx 1800BCE) King Yehoash as directed by Kohen Gadol Yehoyadah wants to collect afresh the chezi-shekel from the people after the 7 year rule of his grandmother Athalia (daughter of Ahab and Jezebel) who ascended the throne after the death of her son Ahaziah. She desecrated the first Temple (Solomon's) with idolatry, e.g. statues of ba'al and associated sacrifices. This was about 150 years after Solomon built the temple and the temple had also fallen into a state of disrepair. With new funds Yehoash wanted to re-dedicate, renovate and reconsecrate the temple. Yehoash ascended the throne at the age of 7 after being secreted away after birth by Yehoyada because Athalia killed off all of her family in order to assume the throne. At 7 years old he gave the Kohanim the responsibility to go and get the shekalim funds for upkeep of the temple and the kohanim were expected to maintain the building either by their own hand or by calling in their own carpenters. However, after 27 years of Yehoash's reign it was apparent that the temple was again falling into disrepair with a suspicion that the funds collected were being pocketed and misused. So Yehoash instituted a system of depositing the shekels in a 'tzedaka box' in the couryard of the temple. An accounting and security system was put in place and funds were distributed to responsible craftsmen who could maintain the temple with the appropriate integrity.
3. Talmud (Shekalim): SACRIFICES and FESTIVALS (Mo'ed). The first mishna of Shekalim (Approx 100CE) recounts how the 1st of Adar (Adar Sheni) was the time when the Beth Din organised officials to go out to Jerusalem, the country and other countries to collect the Shekels for each individual. It was now a shekel, because talmudic period shekels were worth about a biblical half shekel. They had 3 weeks to call in the 'debts' of the shekel and then the money was counted on the first of Nisan. There was also a secondary collection which was for giving as your heart wanted to in order to make the second temple more beautiful. The shekel now was used for the daily communal sacrifices in which everybody participated and had a share in. For outlying areas, if the shekalim could not be brought by the first of Nisan then they were brought before Shavuot or Sukkot. Participation in the daily sacrifice is akin to buying membership to a shul today.