Firstly, the Math function could be done within the if() test loop as that would ignore p == q items.

However, for situations such as this, I would suggest that it is more typical to have two loops - the outer loop going from 0 to the penultimate item and the inner loop going from the outer loop's counter+1 to the last item:

for (let i = 0; i < items.length - 1; i++) {
  for (let j = i + 1; j < items.length; j++) {
    // check values at i and j
  )
}

This way, i and j will never be the same and you never need to iterate over the entire array for every instance of i.

As I mentioned in the comments you can get the same result directly from MongoDB using a MapReduce query; However a cleaner JavaScript equivalent for your nested loops can be something like this:

var data = [
 {"_id": "81724587125","name": "Object 1", "arrayOne":["1","2","3"]},
 {"_id": "87687687687","name": "Object 2", "arrayOne":["4","5","6"]}
];

var result = data.reduce(function (previousValue, currentValue, currentIndex, array) {
    return previousValue.arrayOne.concat( currentValue.arrayOne );
});

As others have already mentioned, Array.prototype.filter() might be the simplest approach (or Array.prototype.reduce() could also be used but would require more conditional logic). It would typically be slower than the nested for loops because it would be adding additional function calls, but for small data sets it typically wouldn't be noticeable. For example, I did a search on Google for "jsperf filter nested loop" and found this jsPerf test.

Using Array.prototype.filter() on A2, pass a callback function that returns true when the value at property value is included in A1 by checking A1.indexOf() for a value greater than -1.

const result = A2.filter(function(o) {
    return A1.indexOf(o.value) > -1;
});

This can be simplified to a single line using an ES-6 arrow function and Array.prototype.includes() (Not supported by IE):

const result = A2.filter(o => A1.includes(o.value));

Try it in this snippet:

var A1  = ["1","2","3","4"];

var A2 = [
    {label:"one", value:"1"},
    {label:"two", value:"2"},
    {label:"three", value:"3"},
    {label:"four", value:"4"},
    {label:"five", value:"5"},
    {label:"six", value:"6"},
];
const result = A2.filter(o => A1.includes(o.value));
console.log('result', result);

If you wanted to use Underscore.js, _.filter() and _.includes() could be used to filter out any object in A2 without a value for the value property contained in A1. Expand the snippet below for a demonstration.

var A1  = ["1","2","3","4"];

var A2 = [
    {label:"one", value:"1"},
    {label:"two", value:"2"},
    {label:"three", value:"3"},
    {label:"four", value:"4"},
    {label:"five", value:"5"},
    {label:"six", value:"6"},
];
const result = _.filter(A2, function(o) { return _.includes(A1, o.value);});
console.log('result', result);

<script src="https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.8.3/underscore-min.js"></script>

There is an Underscore helper _.pluck() but that is used to collect a value from each item in a collection at a given property (similar to Array.prototype.map().

Lodash also has the same helpers: _.filter() and _.includes().

var A1  = ["1","2","3","4"];

var A2 = [
    {label:"one", value:"1"},
    {label:"two", value:"2"},
    {label:"three", value:"3"},
    {label:"four", value:"4"},
    {label:"five", value:"5"},
    {label:"six", value:"6"},
];
const result = _.filter(A2, function(o) { return _.includes(A1, o.value);});
console.log('result', result);

<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.4/lodash.min.js"></script>

Though some question whether libraries like lodash and underscore are really needed anymore. For a discussion on that, check out this article.

Just like Perl,

loop1:
    for (var i in set1) {
loop2:
        for (var j in set2) {
loop3:
            for (var k in set3) {
                break loop2;  // breaks out of loop3 and loop2
            }
        }
    }

as defined in EMCA-262 section 12.12. [MDN Docs]

Unlike C, these labels can only be used for continue and break, as Javascript does not have goto.