Use aura:method to define a method as part of a component’s API. This enables you to directly call a method in a component’s client-side controller instead of firing and handling a component event. Using aura:method simplifies the code needed for a parent component to call a method on a child component that it contains.

Child Component:

<!--Child.cmp-->
<aura:component >
    <aura:method name="messageMethod" action="{!c.getMessage}" access="public">
        <aura:attribute name="param1" type="String" default="Hello"/> 
        <aura:attribute name="param2" type="String" default="World"/> 
    </aura:method>
</aura:component>

Child Component JS Controller:

({
    getMessage : function(component, event) {
        //get method paramaters
        var params = event.getParam('arguments');
        if (params) {
            var param1 = params.param1;
            var param2 = params.param2;
            alert(param1 + " " + param2);
        }
    }
})

Parent Component:

<!--Parent.cmp-->
<aura:component>    
    <div class="slds-m-around_xx-large">
        <!-- Child Component -->
        <c:Child aura:id="childCmp"/>
        <!-- On button click child aura:method will be called-->
        <lightning:button variant="brand" label="Call Aura Method" onclick="{!c.callAuraMethod}" />
    </div>
</aura:component>

Parent Component JS Controller:

({
    callAuraMethod : function(component, event, helper) {
        //Call Child aura method
        var childComponent = component.find("childCmp");
        var message = childComponent.messageMethod();
    }
})

Output: