The Double exclamation idiom converts an expression or or value that is truthy or falsy to a true boolean value. This is discussed in the Essentials section. jQuery uses it in several places throughout its code base. The grep method uses it twice:

grep: function (elems, callback, inv) {
    var retVal,
        ret = [],
        i = 0,
        length = elems.length;
    inv = !!inv;

    // Go through the array, only saving the items
    // that pass the validator function
    for (; i < length; i++) {
        retVal = !!callback(elems[i], i);
        if (inv !== retVal) {
            ret.push(elems[i]);
        }
    }

    return ret;
}

In incoming inv argument is converted to a Boolean and the return value of the callback invocation also.