What is the use of actionfunction ?

A component that provides support for invoking controller action methods directly from JavaScript code using an AJAX request. An <apex:actionFunction> component must be a child of an <apex:form> component.

<apex:page controller="exampleCon">
  <apex:outputPanel onclick="methodOneInJavascript('Yes!')" styleClass="btn">
    </apex:outputPanel>
    <apex:form>
    <apex:actionFunction action="{!methodOne}" name="methodOneInJavascript" rerender="showstate">
        <apex:param name="firstParam" assignTo="{!state}" value="" />
    </apex:actionFunction>
    </apex:form>
</apex:page>

In the above visualforce page javascript method in the on-click event will call the apex controller method with the help of actionfunction.
Apex controller. With the help of actionfunction we can able to make a call to the apex controller class.

public class exampleCon
{
    String uname;
    public String getUsername()
{
        return uname;
    }
    public PageReference sayHello()
{
        uname = UserInfo.getName();
        return null;
    }
    public void setState(String n){
        state = n;
    }     
    public String getState()
{
        return state;
    }
   public PageReference methodOne()
{
        return null;
    }
    private String state = 'no';
}