Need help understanding get/set methods, weird behavior

I have observed Apex properties - a convenient way to implement getters and setters - only being referenced once even though the Visualforce includes multiple references. It seems like there is some caching of values being done but I don't remember seeing any documentation that guarantees that behaviour. So if you want to check the same in your code please do the following changes and check the debug log : -

Apex class

public String  myString{
    get{
        System.debug('-----'+myString);
        return myString;
    }
    set;
}

In Your VF page made below changes :

<apex:page controller="TestController">
   <!-- {!myString}, {!Stringmethod1}, {!Stringmethod2}, {!myString}, {!Stringmethod3}, {!myString}-->
   {!myString},{!myString},{!myString}//make the change by only calling "myString" thrice 
</apex:page>

Now if you open the debug log and check it will only calls once in spite of calling the same thrice from the page.

The first time "myString" is referenced in Visualforce Page is done and the value assigned to the field. On subsequent references the field value is returned without the assignment being done. An advantage of this pattern over setting the properties in the constructor is that if the set of properties referenced varies depending on conditional page logic then only the initialization for the properties that are actually referenced is done so avoiding the waste of calculating the unreferenced properties. The approach works equally well for static fields.

In salesforce "get" method is used to pass data from your Apex code to your Visualforce page and "set" is used to pass data/value from visualforce page to the controller variable.

So basically when you refer a get set variable on VF, the "get" method gets called, and when you change it's value the set method get called.

e.g:
//Apex class
public class GetSetDemo
{  
    public String inputval;
    public String getinputval(){return 'Nil';} //getter for variable

    public void setinputval(String inputval)
    {
        this.inputval = inputval;
    }   
}

//VF
<apex:page controller="GetSetDemo">
  <apex:form>
    <apex:outputlabel value="Enter your name here"/>
       <apex:inputtext value="{!inputval}">
           <apex:actionsupport event="onclick" rerender="display" />
       </apex:inputtext>                   
    <apex:outputpanel id="display">
        <apex:outputtext value="The entered value is {!inputval}"/>
    </apex:outputpanel>                   
  </apex:form>    
</apex:page> 

Now, whatever value you enter the page always displays "The entered value is Nil".... This is because your get method always returns 'Nil'... but still your set method will store the value you entered in the variable "inputval".

So, i entered "Nilesh" in the input field it returns me "The entered value is Nil" because the get method is returning 'nil', but in the apex i am getting it's actual entered value "Nilesh"