RH's post also illustrates the importance of "scaffolding" people when you intend to educate them about furry things. Unfortunately, the internet being what it is, you usually can't just drop the word "furry" into the conversation and then toddle off, because if the explanation you've just given lacks necessary details or important context, of course many people will ask or Google around in an attempt to fill in the blanks.
Usually, my goal is to either make the furry fandom sound so humdrum, so wildly diverse, and/or so charmingly well-intentioned at heart that people won't feel an excessive need to go trawling around for more details.
If people seem curious and eager to learn more, I will actively point them towards the works of specific fursuiters, performers, and artists. My hope and assumption is that if I can help people form a positive first impression of the fandom, they'll be more likely to consider negative or iffy things exceptions to the rule.
Given what's out there on the Interwebs, I would consider telling a person just to Google "furry" sans context to be a VERY BAD IDEA. DO NOT DO THAT.
If I suspect that a person might come into contact with Bad Press or the Dark Side of the Fandom, I might casually mention that furries are an often-stigmatized group, due to the behavior of a few "bad eggs," drama stirred up by some of the younger and/or more socially inept members of the fandom, and the larger society's homophobic tendencies.
After mention this, I will explain that while the community really makes a concerted effort to be accepting and tolerant, the aforementioned "bad eggs" are typically resented and disliked by the wider community, and that the worst ones are eventually banned from conventions and gatherings.