ActionScript is a scripting language primarily used for developing rich internet applications and multimedia content on the Adobe Flash platform. It was developed by Gary Grossman in the mid-1990s and first appeared in Macromedia's Flash 4 software. Over the years, ActionScript has evolved from a simple scripting language to a full-fledged programming language with advanced features and capabilities.

Syntax:
ActionScript syntax is similar to that of JavaScript and C++, making it relatively easy to learn for programmers who are familiar with those languages. ActionScript code is executed by the Flash player, which means that it can be embedded in HTML pages or used as standalone applications.

ActionScript code is stored in files with the extension .as. The basic structure of an ActionScript file consists of the following elements:

- Package: A package is a container that holds related classes and functions. It's similar to a folder in a file system.
- Class: A class is a template for creating objects. It defines the properties and methods that an object will have.
- Method: A method is a function that belongs to a class. It defines the behavior of an object.
- Variable: A variable is a container for storing data.

Example:
Let's look at a simple example of how to write an ActionScript program. This program displays the message "Hello, World!" in a pop-up window when the user clicks a button.

1. Create a new file in Flash Builder and save it as "HelloWorld.as".
2. Add the following code to the file:

```
package {
  import flash.display.Sprite;
  import flash.events.MouseEvent;
  import flash.text.TextField;
  import flash.text.TextFormat;

  public class HelloWorld extends Sprite {
    private var textfield:TextField;
    private var button:Sprite;

    public function HelloWorld() {
      textfield = new TextField();
      textfield.width = 300;
      textfield.height = 50;
      var format:TextFormat = new TextFormat();
      format.size = 18;
      format.color = 0x000000;
      textfield.defaultTextFormat = format;
      textfield.text = "Click the button to say hello!";

      button = new Sprite();
      button.graphics.beginFill(0x008080);
      button.graphics.drawRect(0, 0, 100, 50);
      button.graphics.endFill();
      button.x = 100;
      button.y = 100;
      button.addEventListener(MouseEvent.CLICK, sayHello);

      addChild(textfield);
      addChild(button);
    }

    private function sayHello(event:MouseEvent):void {
      textfield.text = "Hello, World!";
    }
  }
}
```

3. Save the file and run it in Flash Player.

Applications:
ActionScript is used primarily for developing interactive applications, games, and multimedia content on the Flash platform. Some examples of applications that can be developed using ActionScript include:

- Interactive websites and web applications
- Online games and mobile games
- Rich media advertisements
- Educational and training materials
- E-learning courses

ActionScript can also be used in conjunction with other web technologies, such as HTML, CSS, and JavaScript, to create hybrid web applications that combine the best of both worlds.

Conclusion:
ActionScript is a powerful and versatile scripting language that is ideal for developing rich internet applications and multimedia content. With its easy-to-learn syntax and advanced features, ActionScript is an excellent choice for both novice and experienced programmers alike. Whether you're developing a simple website or a complex game, ActionScript provides the flexibility and power you need to bring your vision to life.