Getter and setter methods are used in Java to protect data and make code more secure. Getters return the value of an instance variable, while setters update or set its value. They are also known as accessors and mutators, respectively. By convention, getters start with the word "get" and setters with the word "set", followed by the variable name. In both cases, the first letter of the variables name is capitalized.

Getters and setters allow control over how important variables are accessed and updated in code. They help provide data hiding to prevent direct unauthorized access to variables. Once defined, getters and setters can be accessed inside the main method. They also allow for validation and error handling, which can change the behavior of the data member.

The syntax for a getter method is "public type getVariableName()" and for a setter method is "public void setVariableName(type variableName)". The first letter of the variable name should be capitalized in both cases.

Here is an example of a class with a getter and setter method for a private variable:

public class Vehicle {
    private String color;

    // Getter
    public String getColor() {
        return color;
    }

    // Setter
    public void setColor(String c) {
        this.color = c;
    }
}

In this example, the getter method returns the value of the "color" attribute, while the setter method takes a parameter and assigns it to the attribute.

Overall, getters and setters are important in Java because they allow for better control over how data is accessed and updated in code, which can help improve security and prevent unauthorized access to important variables.