For operators, associativity means that when the same operator appears in a row, then which operator occurence we apply first. In the following, let Q be the operator
a Q b Q c
If Q is left associative, then it evaluates as
(a Q b) Q c
And if it is right associative, then it evaluates as
a Q (b Q c)
It’s important, since it changes the meaning of an expression. Consider the division operator with integer arithmetic, which is left associative
4 / 2 / 3 <=> (4 / 2) / 3 <=> 2 / 3 = 0
If it were right associative, it would evaluate to an undefined expression, since you would divide by zero
4 / 2 / 3 <=> 4 / (2 / 3) <=> 4 / 0 = undefined