Hank here from Shopify.
Just to clarify, is it the meta description associated with your store description, a page, or certain products within your store?
I will share this guide about editing the meta description within your admin, which also has links to set a description for your store. Then, once you have your meta description the way you want it to appear, you will need Google to do a re-crawl of your site. This guide shows how to find, and submit your sitemap which asks Google to re-index your site and update the new information you have submitted.
Google, however, does not advise on how long this process can take, but once you have the update on your end, this helps when the site has been crawled and indexed again.
Let me know how you get on or if you have any additional questions!
All the best,