An expression like 3 + 4 × 2 has no single, self-evident correct answer purely from the symbols themselves; read left to right it gives 14, but calculated by doing the multiplication first it gives 11, and both readings follow perfectly ordinary arithmetic. Order of operations, remembered by the acronym PEMDAS or BODMAS depending on where it's taught, is the fixed, universally agreed sequence, parentheses, exponents, multiplication and division, addition and subtraction, that resolves that ambiguity into exactly one accepted answer, so that mathematicians everywhere reading the same written expression get the exact same result.
Without an agreed sequence, the same expression really would have several valid answers
Mathematical notation, written as a flat string of numbers and operators, doesn't carry any built-in information about which operation should happen first; that information has to come from an external, agreed convention layered on top of the notation, not from the symbols alone. Before that convention existed, mathematicians genuinely could, and sometimes did, read the same written expression differently, arriving at different, individually defensible answers, which caused real practical confusion once mathematics started being communicated in writing across distances rather than worked through together in person.
The specific sequence reflects which operations are defined in terms of which others
The order itself isn't arbitrary: exponentiation is repeated multiplication, so it's resolved before multiplication and division, which are themselves resolved before addition and subtraction, since multiplication is repeated addition. Parentheses sit at the very top of the sequence precisely because they exist specifically to override the default order whenever a calculation genuinely needs a different one, which is exactly why parentheses matter so much in written mathematics: they're the one tool available for deliberately breaking from the standard sequence when a particular calculation actually requires it.
What we're still unsure about
That a fixed, agreed order of operations is necessary to give a written mathematical expression exactly one correct value is well established, and the specific PEMDAS/BODMAS sequence has been taught consistently for well over a century. What's more genuinely a matter of ongoing pedagogical and notational debate is exactly how to handle a small set of genuinely ambiguous edge cases, expressions mixing implicit multiplication with explicit division in certain orders, for instance, where different textbooks and even different calculators can disagree about the intended reading, and mathematics educators continue to recommend writing such expressions with extra parentheses specifically to avoid relying on a convention that isn't, in every single edge case, quite as universally settled as the basic rule usually suggests.
This sits inside Order of Operations (PEMDAS/BODMAS), one of seven topics in Arithmetic, one of seven domains in Mathematics, one of seventeen subjects the app can quiz you on.