Printing object's keys and values

for (key in filters[0]){
    console.log( key + ": " + filters[0][key]);
}

Or if you want to print all the values of filters

for (i in filters){
    console.log(i);
    for (key in filters[i]){
        console.log( key + ": " + filters[i][key]);
    }
}

On @mplungjan 's comment

filters.forEach(function(obj, index){
    console.log(index);
    for (var key in obj){
        console.log(key, obj[key]);
    }
});

This is looking for a term property on filters[0]:

console.log(filters[0].term);

What you actually want to do is use the value of term (in your example that will be "user") as the property identifier:

console.log(filters[0][term]);

for loop for array and for..in iteration for object:

var filters = [{ "user": "abc"}, {"application": "xyz"}];

for (var i = 0; i < filters.length; i++) { // the plainest of array loops
  var obj = filters[i];
  // for..in object iteration will set the key for each pair
  // and the value is in obj[key]
  for (var key in obj) { 
    console.log(key, obj[key])
  }
}

ES6

[{ "user": "abc"}, {"application": "xyz"}].forEach(
  obj => console.log(Object.entries(obj).flat())
)