Sending out emails asking for product reviews is a feature built into the system. This is useful for populating your products with reviews from verified customers.
To set this up, you will first need to have reviews enabled on the store. Take a look at this KB for more information on the Review Functionality.
Setting up Automatic Review Request Emails
To begin, you will want to set up an Email Template asking for the customer to leave a review.
After setting up the email template, go to Settings > Catalog > Product Reviews. In the bottom section, you should see a set of options for the review emails.
First, set the Review Request Email Template to the request review email created earlier. Next, set the Number of Days to Send After. Keep in mind that you want the customer to have time to experience the product before this email sends.
After setting this, go ahead and set the Review Request Trigger. This will be the order status that begins the countdown until the review sends. Most likely you will want to set it to your Shipped status.
Finally, enable the Send Review Request Emails option and Save. Your customers should now begin receiving review request emails based on the settings above.