An operator is something that takes one or more values (or expressions, in programming jargon) and yields another value (so that the construction itself becomes an expression).
Operators can be grouped according to the number of values they take. Unary operators take only one value, for example ! (the logical not operator) or ++ (the increment operator). Binary operators take two values, such as the familiar arithmetical operators + (plus) and - (minus), and the majority of PHP operators fall into this category. Finally, there is a single ternary operator, ? :, which takes three values; this is usually referred to simply as "the ternary operator" (although it could perhaps more properly be called the conditional operator).
A full list of PHP operators follows in the section Operator Precedence. This also explains operator Presedence and Associativity, which govern exactly how expressions containing several different operators are evaluated.