How to refresh the specific Lightning component not the lightning page

If you are refreshing the component from the context of a parent, you don't need to use an event - you can expose a method to the parent and get it to call that.

If you are refreshing the component from within the child itself, you could either use an event or re-run your init routine.

So for a parent calling a public method:

 <aura:method name="reInit" action="{!c.doInit}" description="Runs the init method again ">

The parent could get a reference to the child component and call childComponent.reInit()

For a parent totally refreshing the child, the parent could dynamically recreate the component:

    //clear body of host component just in case
var hostComponent = component.find("enclosingComponent");
hostComponent.set("v.body", []);

$A.createComponent(
  'c:YourChildComponent', {
          "someParam":"someValue"
  },
  function(newComponent, status, errorMessage) {
    //Add the new button to the body array
    if (status === "SUCCESS") {
      var body = hostComponent.get("v.body");
      body.push(newComponent);
      hostComponent.set("v.body", body);
    } else if (status === "INCOMPLETE") {
      console.log("No response from server or client is offline.");
    } else if (status === "ERROR") {
      console.log("Error: " + errorMessage);
    }
  }
);

From the child component If you are doing this from within the component, you can despatch an event to the parent if you want a total refresh, or run the reInit method yourself.

You can define a new COMPONENT event fire it to tell the parent that you want to be refreshed.

<aura:event type="COMPONENT" description="Event used to tell the parent to refresh" >
  <aura:attribute name="componentName" type="string"/>
</aura:event>

In the child component:

<!--markup-->
<aura:registerEvent name="refreshChildComponent" type="c:RefreshChild"/>

//handler
var e = component.getEvent("refreshChildComponent");
e.setParams({ "componentName": "child1"});
e.fire();

In the parent component:

<aura:handler name="refreshChildComponent" event="c:RefreshChild" action="{!c.refreshChild}" />

In the parent helper, the same code as above could be called - in the parent calling a public method section

You are not supposed to refresh one specific component, as the component firing the refresh is not supposed to know what other components are on the page. Instead, create and fire your own event, and handle it in the components that needs to be refreshed.