Groovy is a dynamic programming language that runs on the Java Virtual Machine (JVM). It was developed by James Strachan in 2003 as an alternative to Java that would allow developers to write code more efficiently and with less boilerplate. Groovy combines features from Java, Python, and Ruby to provide a language that is both powerful and easy to learn.

Biography of Groovy:
Groovy was first released in 2003, with the goal of making Java development more enjoyable and productive. It quickly gained popularity among Java developers, as it allowed them to write code faster and with fewer lines of code than Java. Groovy was influenced by many programming languages, including Java, Python, and Ruby. One of the key features of Groovy is its support for dynamic typing, which allows developers to write code more quickly and with less overhead than Java.

Syntax and Example:
Groovy's syntax is very similar to Java's, with some important differences. One of the main differences is that Groovy is more concise, with less boilerplate code. For example, a simple "Hello, world" program in Java would look like this:

```
public class HelloWorld {
   public static void main(String[] args) {
      System.out.println("Hello, world");
   }
}
```

In Groovy, the same program can be written like this:

```
println 'Hello, world'
```

As you can see, the Groovy version is much shorter and easier to read. Groovy also has many features that Java doesn't, such as closures, dynamic typing, and operator overloading.

One of the most powerful features of Groovy is its support for domain-specific languages (DSLs). A DSL is a programming language that is tailored to a specific domain or problem space. Groovy makes it easy to create DSLs, which can greatly simplify complex tasks. For example, Groovy includes a built-in DSL for creating HTML pages:

```
html {
   head {
      title "My Web Page"
   }
   body {
      h1 "Welcome to my web page"
      p "This is a paragraph of text"
   }
}
```

This code creates an HTML page with a title and some text. The syntax is very concise and easy to read.

Applications of Groovy:
Groovy has many applications in software development, including web development, scripting, and testing. Groovy is often used to write scripts that automate repetitive tasks, such as build scripts or deployment scripts. Groovy is also commonly used for web development, as it has built-in support for creating web applications using the Grails framework. Groovy is also widely used in testing, as it makes it easy to write unit tests and integration tests.

Conclusion:
Groovy is a powerful and flexible programming language that is easy to learn and use. Its concise syntax, support for dynamic typing, and DSL capabilities make it a popular choice for Java developers who want to write code more efficiently. Groovy has many applications in software development, including web development, scripting, and testing. If you're looking to learn a new programming language, Groovy is definitely worth considering.