Below are some reasons arguing for the use of the pattern and example code in Java, but it is an implementation of the Builder Pattern covered by the Gang of Four in Design Patterns. The reasons you would use it in Java are also applicable to other programming languages as well.

As Joshua Bloch states in Effective Java, 2nd Edition:

The builder pattern is a good choice when designing classes whose constructors or static factories would have more than a handful of parameters.

We've all at some point encountered a class with a list of constructors where each addition adds a new option parameter:

Pizza(int size) { ... }        
Pizza(int size, boolean cheese) { ... }    
Pizza(int size, boolean cheese, boolean pepperoni) { ... }    
Pizza(int size, boolean cheese, boolean pepperoni, boolean bacon) { ... }

This is called the Telescoping Constructor Pattern. The problem with this pattern is that once constructors are 4 or 5 parameters long it becomes difficult to remember the required order of the parameters as well as what particular constructor you might want in a given situation.

One alternative you have to the Telescoping Constructor Pattern is the JavaBean Pattern where you call a constructor with the mandatory parameters and then call any optional setters after:

Pizza pizza = new Pizza(12);
pizza.setCheese(true);
pizza.setPepperoni(true);
pizza.setBacon(true);

The problem here is that because the object is created over several calls it may be in an inconsistent state partway through its construction. This also requires a lot of extra effort to ensure thread safety.

The better alternative is to use the Builder Pattern.

public class Pizza {
  private int size;
  private boolean cheese;
  private boolean pepperoni;
  private boolean bacon;

  public static class Builder {
    //required
    private final int size;

    //optional
    private boolean cheese = false;
    private boolean pepperoni = false;
    private boolean bacon = false;

    public Builder(int size) {
      this.size = size;
    }

    public Builder cheese(boolean value) {
      cheese = value;
      return this;
    }

    public Builder pepperoni(boolean value) {
      pepperoni = value;
      return this;
    }

    public Builder bacon(boolean value) {
      bacon = value;
      return this;
    }

    public Pizza build() {
      return new Pizza(this);
    }
  }

  private Pizza(Builder builder) {
    size = builder.size;
    cheese = builder.cheese;
    pepperoni = builder.pepperoni;
    bacon = builder.bacon;
  }
}

Note that Pizza is immutable and that parameter values are all in a single location. Because the Builder's setter methods return the Builder object they are able to be chained.

Pizza pizza = new Pizza.Builder(12)
                       .cheese(true)
                       .pepperoni(true)
                       .bacon(true)
                       .build();

This results in code that is easy to write and very easy to read and understand. In this example, the build method could be modified to check parameters after they have been copied from the builder to the Pizza object and throw an IllegalStateException if an invalid parameter value has been supplied. This pattern is flexible and it is easy to add more parameters to it in the future. It is really only useful if you are going to have more than 4 or 5 parameters for a constructor. That said, it might be worthwhile in the first place if you suspect you may be adding more parameters in the future.

I have borrowed heavily on this topic from the book Effective Java, 2nd Edition by Joshua Bloch. To learn more about this pattern and other effective Java practices I highly recommend it.

It's so you can be immutable AND simulate named parameters at the same time.

Person p = personBuilder
    .name("Arthur Dent")
    .age(42)
    .build()
;

That keeps your mitts off the person until it's state is set and, once set, won't let you change it. Yet every field is clearly labeled. You can't do this with just one class in Java.

It looks like you're talking about Josh Blochs Builder Pattern. This should not be confused with the Gang of Four Builder Pattern. These are different beasts. They both solve construction problems, but in fairly different ways.

Of course you can construct your object without using another class. But then you have to choose. You lose either the ability to simulate named parameters in languages that don't have them (like Java) or you lose the ability to remain immutable throughout the objects lifetime.

Immutable example, has no names for parameters

Person p = new Person("Arthur Dent", 42);

Here you're building everything with a single simple constructor. This will let you stay immutable but you loose the simulation of named parameters. That gets hard to read with many parameters. Computers don't care but it's hard on the humans.

Simulated named parameter example with traditional setters. Not immutable.

Person p = new Person();
p.name("Arthur Dent");
p.age(42);

Here you're building everything with setters and are simulating named parameters but you're no longer immutable. Each use of a setter changes object state.

So what you get by adding the class is you can do both.

Validation can be performed in the build() if a runtime error for a missing age field is enough for you. You can upgrade that and enforce that age() is called with a compiler error. Just not with the Josh Bloch builder pattern.

For that you need an internal Domain Specific Language (iDSL).

This lets you demand that they call age() and name() before calling build(). But you can't do it just by returning this each time. Each thing that returns returns a different thing that forces you to call the next thing.

Use might look like this:

Person p = personBuilder
    .name("Arthur Dent")
    .age(42)
    .build()
;

But this:

Person p = personBuilder
    .age(42)
    .build()
;

causes a compiler error because age() is only valid to call on the type returned by name().

These iDSLs are extremely powerful (JOOQ or Java8 Streams for example) and are very nice to use, especially if you use an IDE with code completion, but they are a fair bit of work to set up. I'd recommend saving them for things that will have a fair bit of source code written against them.