Maybe you've received an email like that, and you are pleased and surprised. You put their little html graphic and link on your web page to proudly display that you are a "great cat shelter" or "great cat rescue" or just a downright "great person" or "great blogger."
Sometimes these awards are legit. They will usually mention something about you--an exact blog post you wrote, or something special you did. But quite often they are just a way for you to become a free portal to a web site that hosts Google ads. They want visits to their site generated by your page, so that visitors (your readers) will click on a Google ad and get them money.
That's all. Sad, isn't it?
So the next time your are offered an "award"..go visit the page offering it. If it hosts lots of ads, like Google ads, and especially if the "award" code is on their page available for anyone to pick up...it's no honor. They don't mind if just anyone lifts the code and posts their "award" because all they want is more traffic. They don't want to honor you. They want to use you. You'll often find that these web sites haven't even screened out puppy-mill ads from their Google ads (an option they have), and that this web site that told you that you do such great work rescuing animals, is actually making money from puppy-mill and for-profit breeder ads.
Does that mean anyone hosting Google ads is bad? Absolutely not. Just make sure if you are directing traffic to a site with Google ads, that you are doing so knowingly, and the ads are those you would want your readers to visit.