How to get the value of variable in different javascript file?

Your code hints at a namespace pattern but falls slightly short.

You might like to consider something like this

var TAP = (function($) {//functional namespace
  var settings = {
    hold_threshold: 750,
    hold_timer: null,
    timer: null
  };
  var setSettings = function(s) {
    settings = $.extend(settings, s);
  };
  var getSettings = function() {
    return settings;
  };
  return {
    set: setSettings,
    get: getSettings
  };
})(jQuery);

Thus, TAP has private member settings and public members set() and get(). You will see that further private and public members are easily added.

Now you have a mechanism to both set and get TAP settings from anywhere that TAP is within scope:

TAP.set({hold_threshold: 500});

var Navigation = {
  init: function () {
    self = this;
    $('#button').live(tapMode, function () {
      alert(settings[TAP.get().hold_threshold]);
    });
  }
}

With TAP as a member in the global namespace, it's public methods are available in all scopes.

More typically, you will use the MODULE pattern, which puts just one PROJECT member into the global namespace, containing any number of MODULES, each containing any number of functional NAMESPACES, for example :

var MYPROJECT = {};//global
MYPROJECT.MODULE1 = {};
MYPROJECT.MODULE1.TAP= (function($) {
  var settings = {
    hold_threshold: 750,
    hold_timer: null,
    timer: null
  };
  var setSettings = function(s) {
    settings = $.extend(settings, s);
  };
  var getSettings = function() {
    return settings;
  };
  return {
    set: setSettings,
    get: getSettings
  };
})(jQuery);

By convention, MYPROJECT, its MODULES and its functional NAMESPACES are capitalized.

settings is nested within a closure and it cannot be accessed from the outside. One solution is to remove the closure so that it becomes a global object. Another solution is to assign it to the window object, same as making the variable global but this works from inside closures. Here is an example:

(function ($) {
    window.my_namespace = window.my_namespace || {};
    window.my_namespace.settings = {
        taphold_threshold: 750,
        hold_timer: null,
        tap_timer: null
    };
});

var Navigation = {
    init: function () {
        self = this;
        $('#button').live(tapMode, function () {
            alert(my_namespace.settings[taphold_threshold]);
        });
    }
};

Since var settings is defined in test1.js inside a closure, hence the problem exists.

You might want to define the settings variable as

window.settings = ...

OR

window['settings'] = ...

So now settings would be defined as a global variable.