The associative property of addition says that it does not matter how we group the addends when we add 3 or more numbers. My question is, does addition only operate on 2 numbers at a time?(binary operator)
I don't know if the term "binary operator" exists, I am new to algebra. If they exist, could you give me examples of binary operators?
I do not agree with Arturo's comment. Everyone knows what addition of $n$ numbers means intuitively: for example, if I have $n$ sticks each of length $\ell_1, \ell_2, \dots \ell_n$ and I put them all in a line then I get a big stick of length $\ell_1 + \ell_2 + \dots + \ell_n$, and so forth. Addition is a perfectly well-defined $n$-ary operation for every $n$ and this is something we understand before anyone tells us anything about associativity.
The significance of associativity is that it lets us reduce all of these operations to a single binary operation $a + b$, because we can get the larger operations from it, e.g. ternary addition $\ell_1 + \ell_2 + \ell_3$ is either $\ell_1 + (\ell_2 + \ell_3)$ or $(\ell_1 + \ell_2) + \ell_3$. In terms of sticks this means I can put $n$ sticks together by putting them together in pairs and it doesn't matter how I do this.
It's convenient to do this reduction-to-the-binary-operation thing because it means we only have to talk about a binary operation instead of a whole family of $n$-ary operations which is in some sense redundant. But sometimes it's worth going all the way up to the whole family of $n$-ary operations to remind ourselves why things like associativity are supposed to be true in the first place.