Hi,

Greetings to you!

Please try the below code, I have tested in my org and it is working fine. Kindly modify the code as per your requirement.

Component:

<aura:component controller="DatatableButtonIconC"
                implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId,forceCommunity:availableForAllPageTypes,force:lightningQuickAction" access="global" >
    
    <aura:attribute name="dataList" type="Object" />
    <aura:attribute name="columnsList" type="List" />
    
    <aura:handler name="init" value="{! this }" action="{! c.init }" />
    
    <div class="slds-is-relative">
        <lightning:datatable keyField="Id"
                             data="{! v.dataList }"
                             columns="{! v.columnsList }"
                             hideCheckboxColumn="true" 
                             onrowaction="{! c.handleRowAction }"/>
    </div>
</aura:component>

Controller:

({
    init: function (component, event, helper) {
        var columns = [
            {
                type: 'button-icon',
                fixedWidth: 40,
                typeAttributes: {
                    iconName: 'utility:description',
                    name: 'show_record', 
                    title: 'Show',
                    variant: 'border-filled',
                    alternativeText: 'show',
                    disabled: false
                }
            },
            {
                label: 'Name', 
                fieldName: 'Name', 
                type: 'text'
            }
        ];
        var action  = component.get("c.getContactsList");
        action.setCallback(this,function(response){
            var result = response.getReturnValue();
            component.set('v.columnsList', columns);
            component.set("v.dataList", result);
        });
        $A.enqueueAction(action);
    },
    
    handleRowAction :function(cmp,event,helper){
        //action gives which action performed
        var action = event.getParam('action');
        //row gives complete row information
        var row = event.getParam('row');
        console.log('*****row:'+JSON.stringify(row));
        console.log(JSON.stringify(action));
        alert('You have selected View Action for '+row.Name+'(id='+row.Id+')');
    }
})

Apex:

public class DatatableButtonIconC {
    
    @AuraEnabled
    public static List<Contact> getContactsList() {
        return [select Id,Name from Contact limit 10];
    }
}

I hope it helps you.

Kindly let me know if it helps you and close your query by marking it as solved so that it can help others in the future. It will help to keep this community clean.

Thanks and Regards,
Khan Anas