I don't know - that's just what they call it. I guess it makes people feel noble or something. If anything, the animal rescues YOU. But it's not free. There's no such thing as a free pet. Along with the standard 'adoption fees,' you also shell out money for their medical care, spaying, grooming, toys and food, and it aint cheap. But it's the best money you'll ever spend. I'd say altogether, with the two dogs and now the two cats, it's about $1000 a year. (I buy the best foods though so yours might be cheaper.) But when you think about all the love and laughter they bring into your life, that is nothing. NOTHING.
It is a bit like a rescue though when the fate of the animal without you in the picture is bleak. Sasha-Bear was "for sale" by a family in Casa Grande who didn't know shit about breeding or puppies. She was a purebred, but there were no AKC papers. The family was moving, spoke very little English, and wanted $300 for each puppy. But they did not want to keep the puppies with the mother for the standard minimum of 8 weeks. This is very detrimental to the puppies. We drove out to see her, afraid of what we were going to find because the price was so low. The mother dog was there - she was filthy and matted and the father was locked in the back yard, equally unkempt - stuck out in the heat. It was not a good scene. We gave them the money up front and begged them to hold the pup with her mother a bit longer but they refused. So I took Sashi home at 5 weeks, and fed her raw goat's milk from a local farm to try and supplement the nutrients and antibodies she should have received from her mother's milk. I also tried to socialize her as best I could, but there's no substitute for the mother's training and the nips and responses from litter mates. Sasha came out fine, although she is very slow to warm up to strangers and very possessive. The point is I guess that you rescue them, and they rescue you. Like the line in Pretty Woman - LMFAO.
http://i.imgur.com/MRDdv.jpg