The logo designation is part of the Organization markup within schema.org. Using it will allow Google algorithms to understand which image on your server is your preferred logo. If you used such a file on your home page, you can designate it directly from the same IMG tag you use on your site.
The tag markup looks like this:
<div itemscope itemtype="http://schema.org/Organization">
<a itemprop="url" href="http://www.example.com/">Home </a>
<img itemprop="logo" src="http://www.example.com/logo.png"/>
From their example code, it also appears that Google is advocating for site owners to link their company logo to the home page, a practice not every site implores.
An interesting discussion has already broken out about the new markup. Some websites use logo images as a background style to a header using CSS instead of an explicit IMG tag. The Google help documentation didn't directly address this issue. An answer to that question would be most helpful to many webmasters.
According to Google's engineers, once you designate a preferred logo using the Organization schema, your logo "may be used in Google search results" and "is a strong signal to ... show this image in preference over others." Google's post specifically mentions Knowledge Graph results as an example of where your organization's logo may be used.
This change is likely an indication that Google may be expanding their Knowledge Graph results in the near future. Or, Google could possibly extend images next to search results, similar to what is currently done for authors using authorship markup. Recently, Bing began experimenting with images in search results, similar to authorship markup, but also for news results.