facebook will use the meta-description tag for a shared link's description when no Open Graph description tag is present. I use meta description in hopes it's used by Google, it does get used much more by Bing and other SE's.
facebook will display 3 lines of description text, which might be upwards of 200 characters before showing the "More..." link. Clicking will show the rest up to 299 characters.
As this has been asked in the General Search Engine Marketing area, I must assume that this is not a Google specific question but relates to all search engines globally.
Whereas the information posted for Google is correct, I must point out that some other search engines do attach ranking significance to the description tag and some (such as Baidu) to the keyword tag. Although for Western language sites the keyword tag really has no relevance, if you are intending to be picked up by certain non-western SEs, the keyword tag can assist slightly. However, my maxim for the keyword tag is if in doubt of how to use it for a specific engine, leave it out.
The description tag does have an impact on ranking on some other search engines and allows you to at least be able to structure a meaningful 'invitation' to a searcher even on Google which will display the description tag on occasions. For that reason alone, it is worth using, IMO.