It is not recommended to try and understand the Jeju 4.3 Incident through a summarized form due to the large amount of complexities that are related to why it happened, what happened, and the aftermath. However, if you are trying to get a 'birds eye view' of it before learning more, then you can start here.
What caused Jeju 4.3?
The Jeju 4.3 Incident was caused by a series of local issues: torture and harassment by the police (with no repercussions), a struggling economy, the re-emergence of pro-Japan policemen and officials, the increasing marginalization of local viewpoints in governance as well as national issues such as the split of the country into North and South Korea.
What was Jeju 4.3?
Following a year of protests, arrests, and torture, on April 3, 1948 armed members of the South Korea Labor Party Jeju branch attacked police stations and right wing militant groups due to a number of local and national issues (see above). They believed that there was no other way to send a strong enough message to the government that the situation had become intolerable. After a few months of stalemate fighting, the police and army began to ramp up the aggressiveness of the suppression methods used, leading to the deaths of hundreds to thousands of civilians. In the fall/winter of 1948 and into early 1949, tens of thousands of Jeju civilians were killed in the name of suppressing and ending the (allegedly) communist armed resistance.
What happened after 4.3 ended?
The fighting in Jeju largely ended in June 1949 after the death of the second commander of the armed resistance, Lee Deokgu. Officially, Jeju 4.3 ended in 1954 when the ban on the entry to Halla Mountain was lifted. During that period (1949 - 1954) many hundreds to thousands more Jeju civilians were killed during the Korean War - again in the name of fighting communism. After that the government tried to sweep the Jeju 4.3 Incident 'under the rug'. They were largely successful as a generation of Koreans grew up not knowing that such an event happened. In Jeju, the topic became incredibly taboo to speak of and doing so brought swift consequences.
The discovery of Darangshi Cave in 1991/1992 was one of the first major events that led to people learning about Jeju 4.3. In 1998, President Kim Daejung called for a special investigation into 4.3, and the National Assemby passed a law a year later in 1999 that would allow the government to begin investigating. That process began in 2003, and the same year President Roh Moohyeon became the first sitting president to apologize for the incident. President Moon Jaein did the same when he became president, and in 2019 the Defense Ministry and police also officially apologized for the incident as well. However, even today legal challenges and consequences to 4.3 are still being played out in the South Korean courts.