In short: a meta description is a 160 character "elevator pitch" (or summary) on why a user should click and visit your webpage. They show up under a title tag when a user is searching for a thing and your webpage is one of the results they get back.
The search engine will cut off the meta description and adds an ellipse exactly at the 160 character cut-off point. On occasion the search engine will show more than 160 characters, but generally speaking, 160 is the max—so make your point clearly and quickly.
If the meta description is not optimized at all, the search engine will sometimes just choose a random snippet from the page content to use as the meta description.
So do your best to optimize the page descriptions to the best of your abilities. Be concise and don't use any unnecessary adjectives, adverbs or punctuation marks. Also, make sure that the content of the meta description accurately reflects the content of the page, otherwise the user will bounce.
The most important thing to keep in mind when crafting meta descriptions is to write a compelling, and truthful summary of why a user should visit your website to find the answer to their question.
Related Content:
How to Write Title Tags for SEO