To put it simply as I possibly can, a furry is a person who, for many of various possible reasons, feels a strong affinity towards a certain non-human animal species and usually that they are somewhat more animal than human. There are many extremes to this, but that's the simplest answer I can come up with.
Often, one who calls themself furry has a "fursona," a fictional representation of themself, most commonly an anthropomorphic (or human-like with animal qualities) character. I wouldn't necessarily go as far as to exclude those who tend towards a feral-sona, but in my mind, it's usually an anthro character.
It might be a good thing that you're somewhat hesitant about googling it; much of the outside view of furries isn't necessarily positive. (see the CSI episode (fur and loathing) to get what I mean)
