If a date is appearing at the beginning of your site’s description on a Google search results page, there is a probably a good reason why. Some site sites want these dates to appear such as blog posts, news sites, forums, etc., because the dates help the users to determine how relevant the information behind the link might be. In other cases Google has for one reason or another determined the results page would be enhanced by adding a date to the description, but for the site owner it can seem more than irrelevant.
We recently had a situation where an eCommerce client of ours starting having dates appear at the beginning of their description on Google search result pages after a site redesign. After much research we determined that links to certain RSS feeds from the homepage (which were added during the re-design), might be the culprit. The feeds were for content such as new customer reviews, new products, etc and were updated each day. The dates we were noticing in the descriptions seemed to change all they time and stayed fairly recent. We remove the links to the RSS feeds and viola, no more dates in the Google descriptions!
There are probably many other places Google could grab a date to associate with the description such as the Last-Modified variable in the header, other dates included in your content, dates in the URLs of blog posts, and many others I am not thinking of right now.