A class is a compilation unit, and it combines both properties (member variables) and behavior (methods). The best way to think of it as a blueprint. You write one class, and from that, are able to create as many instances (objects) as you want. They all act the same, but represent a different entity.

Code:
public class Dog {
   private String name;

   public Dog(String name) {
      this.name = name;
   }

   public String getName() {
      return name;
   }

   public void bark() {
      System.out.println("woof!");
   }
}
That class represents (duh!) a dog. In this case, all dogs have a name (the properties), and are able to bark (behavior).

With this, you can do something like:
Code:
Dog cobi = new Dog("Cobi");
Dog dog2 = new Dog("Fido");

cobi.bark();
dog2.bark();
So basically, a class allows you to create a blueprint for some entity. Then you use it to define particular instances, which act the same way, but have different state. It's a good way to model real-world objects.

The best thing you can do is pick up a copy of Thinking in Java , by Bruce Eckel. And the beautiful thing is that he offers it for free on his website. So go download that, read through it, and you're well on your way.