In this instance, the ~ allows that code to turn the return value of .indexOf() — which is a number indicating the position of the searched-for value in the array — into a boolean. In other words, it takes the "where is the value" result and turns it into a "is the value in the list" result.
How?  Well, .indexOf() returns -1 when the value is not found, and a number greater than or equal to zero if it is. The ~ operator converts its numeric argument to a 32-bit integer and then inverts every bit. That process happens to turn -1 to 0, and any positive integer to some negative non-zero value, and 0 to -1.  When such results are subsequently examined as boolean values, the original -1 will be false (because 0 is "falsy") while the integers greater than or equal to zero will be true (because they're all converted to some non-zero value).