Why is the word associative used to represent the concept of the associative property?

I think Hamilton came up with the term "associative," probably as a result of thinking about the (now-called) octonions that Cayley was writing to him about. If you'll allow me to speculate, I think it's likely it's because in parenthesized expressions such as $a(bc)$, two terms that are immediately concatenated together can be called "associated" in the standard English meaning of the term.

In French, associer means making links and connections. Therefore, associative literally means tending to make links and connections. If $\star$ is an associative law, one has: $$(a\star b)\star c=a\star(b\star c).$$ With an associative law, you get the same result regardless of the pairwise associations.