This is very basic and your question is incomplete.
first, you need a button for approval (maybe in a @foreach block)
<a onclick="approve(<row id>)" class="your_button_class">Click to Approve!</a>
then you need a script
<script>
function approve(id)
{
$.ajax({
//some ajax call to deal with your approve link
type: 'post',
url: 'route to update data',
data: "id="+id,
success: function (data) {
alert('updated');
}
});
}
</script>
In your controller
function update(Request $request)
{
$id=$request->id;
$model = new YourModel();
//assumed your column is "approved" and approved status is "0"
$updated = $model->find($id)->update(['approved'=>1]);
return $updated;
}
use this reference to build your logic.
or see this example