Mexican voters face a daunting task on Sunday.

For the first time in the country’s history, they will elect more than 2,600 judges and magistrates, including those who will sit on the Supreme Court and hundreds of other federal, state and local tribunals.

The election will move the judiciary from an appointment-based system to one in which voters will choose their judges. Supporters of the overhaul argue it makes the system more democratic and counteracts problems like nepotism and corruption. Critics say it risks giving the governing party more power and opens the courts to candidates who lack experience and qualifications, or could be influenced by criminal groups like cartels.

The experiment is so ambitious, divisive and confusing that it is difficult to know how it will unfold: A single day of voting will enact the most far-reaching judicial overhaul ever by a large democracy.

Here’s what to know about Mexico’s election for judges, how it works and why it matters.

Why are Mexicans voting for judges?

The election is the culmination of a contentious process in which Morena, the governing party, and its allies amended the Constitution last year to overhaul the court system.

The idea to elect judges by popular vote was proposed by President Andrés Manuel López Obrador and championed by his successor, Claudia Sheinbaum.

Mr. López Obrador pushed the plan after the Supreme Court issued a series of rulings that blocked some of his government’s plans — such as weakening Mexico’s electoral watchdog agency and putting the National Guard under military control — and federal judges issued orders to suspend some of his flagship projects, citing environmental concerns.