Construct 2 allows you to import external files to your project. For more information, see the manual entry on Project Files. This tutorial covers some useful workflows for using project files.
Using external image files
If your project has a lot of large detailed images which add a lot to the download size, you can make your game load quicker by adding them as project files instead. That way they won't need to be downloaded before the game starts running. You can then load them at runtime using Sprite or Tiled Background's Load image from URL actions - just enter the name of the image as the URL, e.g. "mylargeimage.jpg". You know they've loaded when the On image URL loaded trigger fires as well. This means you can request large images on the start of each layout that needs them, and show some kind of "Please wait..." message until they've loaded.
Using files for third party plugins
You may have third party plugins like a video plugin that can play videos. You can add the videos or any other files the plugins can use as project files, and access them using their filename as the URL, e.g. "myvideo.ogv". This works because all project files are in the same folder when exported, so their filenames can be used as relative URLs.
Storing additional web pages with your project
You may want to have a few extra simple HTML pages stored with your project. You can import any necessary extra HTML, CSS and Javascript files to your project, and browse to them with the Browser object. Please note that folders in Construct 2's project bar are for organisation only - once exported, all files are in the same relative folder, regardless of their folder in the Project Bar.
Loading XML data
If you want to read an XML file stored with the project, import the XML file as a project file. Then you can use the AJAX object's Request project file action to download the file, and then load the result in to the XML object. The events below show how this can be done.
Storing additional documents or files to download
You can store PDF documents or other files with your project, and use the Browser object to download them (open the filename as a URL in a new window).
Making level editors
Perhaps the most advanced use of project files is the ability to support your own custom level editor. This can even include user-made levels, creating a community of additional level designers for your game, and increasing its longevity!
Making a level editor is complicated, and won't be covered in full detail here. However the principle is that using the Array, Dictionary or XML objects (or some combination of them), you can store data representing an entire level. If you've designed your level editor in Construct 2, you can use Array or Dictionary's Download action to download a .json file storing the data, or simply use their AsJSON expressions to get the data as a long JSON string. Once you have a file or files representing a level, you can import them as project files, e.g. level3.json.
Once you have all your levels imported, you can load them by requesting them with the AJAX object then loading the result in to the object, similar to how is done with the XML object in the above example. Then you are ready to load the level.
The cool thing about this is you can allow for user-made levels. If a user designs a level and uploads it somewhere like http://www.example.com/usermadelevel.json, you could have a text field in your game where you enter this URL and load their level.
You can also allow yourself to change or add new levels after the game is published, without re-uploading the entire game. For example if you load a list of available levels from an XML file, you only need to upload or change a few .json files then edit the .xml file in order to add or update levels.
Don't forget project files are available during preview, and are also cached for offline use, so it's easy to test and doesn't cause any trouble for offline players either.
One last tip: you can combine multiple arrays in to a single .json file using the Dictionary object. Simply store keys in the Dictionary object which store each array as JSON data, e.g.
Set "array1" to Array1.AsJSON
Set "array2" to Array2.AsJSON
Set "array3" to Array3.AsJSON
Then you can add a few extra keys (e.g. the name of the level) and download everything as a single .json file from the Dictionary object.
Conclusion
Project files are a very powerful feature of Construct 2 with a lot of flexibility. It allows for a lot of interesting new capabilities, such as dynamic image loading, better support for third party plugins, convenient handling of additional pages or documents, and even making full blown level editors with support for user-made levels. There are doubtless other things you can use it for other than those listed here - post your ideas in the comments!