These two characters combine powerfully: 叛 (a betrayal) leads directly to 乱 (chaos). Therefore, 叛乱 describes a rebellion that is seen as both an act of treachery and a source of societal disorder.
In Chinese history and political thought, the concept of 叛乱 is deeply tied to the “Mandate of Heaven” (天命, Tiānmìng). For millennia, an emperor's right to rule was believed to be granted by a divine power. A successful rebellion was often interpreted retroactively as proof that the old dynasty had lost this mandate due to corruption or incompetence, and the new leader had gained it. This contrasts with the Western concept of “revolution” (like the American or French Revolutions), which is often framed with positive ideals like liberty, rights, and progress from the outset. 叛乱, from the perspective of the established government, is always a crime of the highest order—an act of treason that threatens social harmony and stability (稳定, wěndìng), which are paramount values in Chinese culture. Essentially, history is written by the victors. What a failing dynasty calls a treacherous 叛乱, a successful new dynasty will call a glorious 起义 (qǐyì - righteous uprising) or 革命 (gémìng - revolution). The term 叛乱 itself is a label applied by those in power to delegitimize their opponents.
This is a formal and serious term. You will almost never hear it in casual conversation.
The most common mistake for learners is confusing 叛乱 with other forms of opposition.