For instance, in “Programming Perl”, there are sentences such as this one:
These string operators bind as tightly as their corresponding arithmetic operators.
In other places, both in “PP” and in perldoc, the authors use phrasing such as “binds tightly”; for instance, when referring to =~, or “binds even more tightly” when referring to ** (exponentiation).
If this were the same as precedence, it would not be possible to say things like “even more tightly”, I’m guessing. You’d say “higher/lower precedence” instead.
So what exactly does it mean for an operator to bind?
This refers to operator precedence. In the statement
The multiplication has higher precedence, and therefore “binds” more tightly than addition.
Operators that bind more tightly are evaluated before less-tightly bound operators.