function updateData(){
  var dirReader = approot.createReader();

  var fail =failCB('Error - Directory for parsing failed to open'); // logs fail...
  dirReader.readEntries(parseData,fail);
}

function parseData(entries){
  var i;
  for (i=0; i<entries.length; i++) {
    var reader = new FileReader();
    reader.onloadend = createListItem;
    reader.readAsText(entries[i]);
  }
}

function createListItem(evt){
    // it gives me all the loaded data. But based on wich file it was, i would like to handle it!
  console.log(evt.target.result)
    // lets say something like this
    $('#content').find(   file.name   ).append(evt.target.result);
  }
}

function parseData(entries){
  for (var i=0; i<entries.length; i++) {
    reader.onloadend = (function(file) {
      return function(evt) {
        createListItem(evt, file)
      };
    })(entries[i]);
    reader.readAsText(entries[i]);
  }
}

function createListItem(evt, file) {
  console.log(evt.target.result)
  console.log(file.name);
}

for(i=0; i < files.length; i++)
    {
        var fileReader = new FileReader();
        fileReader.onload = function(file)
        {
              // DO what you need here
              // file name = file.target.fileName
        } // end of reader load
        fileReader.fileName = files[i].name;
        fileReader.readAsBinaryString(files[i]);
    }

for (var i = 0; i < files.length; i++) {

    var fileReader = new FileReader();

    fileReader.fileName = files[i].name;

    fileReader.onload = function () {
        /* do something with file */
    }

    fileReader.onloadend = function () {
        console.log(fileReader.fileName); // here you can access the original file name
    }

    fileReader.readAsText(files[i]);

}