The meta description is a short phrase that summarizes the topic of the page.
Meta descriptions go in the <head> of a page, in the format: <meta name="description" content="Search Engine Optimization: make your pages succeed in search results and for human beings."/>
Sometimes a search result will show a meta description below the link to that page, and sometimes it will show a person's search terms in bold, in the context of an excerpt from the page. Meta descriptions may also be used by social media, for example when a particular page is shared on Facebook.
Before you add meta descriptions to every page, take note that while good meta descriptions are better than none, bad meta descriptions can hurt your site.
If meta descriptions are the same for a lot of pages (or break other Google recommendations), they may be ignored entirely, and they'll certainly be less useful for users.
Descriptions are often cut short in search results, so front-loading important words is vital. Eliminate "filler" text like, "This page is intended to..." or "Here you'll find." Cut right to the chase, and identify the precise content of that specific page.
DaniWeb likens meta descriptions to "a permanent Tweet for your website" and that's a good way to think about it: write an "elevator speech" for your page.
The meta "keywords" tag is largely ignored these days (as it was so hideously abused by people trying to capture search results for which they weren't really relevant), but including key words in your text is a good idea.