1. The problem is to understand what the non-associativity of octonions means. 2. Octonions are an extension of complex numbers and quaternions, forming an 8-dimensional algebra over the real numbers. 3. Associativity is a property of multiplication where for any three elements $a, b, c$, the equation $(ab)c = a(bc)$ holds. 4. Non-associativity means this property does not hold for octonions; that is, there exist octonions $a, b, c$ such that $(ab)c \neq a(bc)$. 5. This implies that when multiplying octonions, the order in which you perform the multiplications matters. 6. Despite this, octonions are alternative, meaning the associator $(a,b,c) = (ab)c - a(bc)$ is zero if any two of $a,b,c$ are equal. 7. This non-associativity makes octonions more complex and less intuitive than real numbers, complex numbers, or quaternions, but they have important applications in advanced mathematics and theoretical physics. Final answer: Non-associativity of octonions means that multiplication of octonions does not always satisfy $(ab)c = a(bc)$, so the grouping of factors affects the result.