Tail sniffing behavior is normal between cats and cat butt presentation is a part of cat talk. But it often surprises us when Fluffy leaps onto our lap for a petting session, turns around, and presents his (ahem) furry nether regions.
Why Cats Show Their Butt
Think of this from your cat's perspective. When greeting each other for the first time (after the hissing stops!), cats sniff each other's face and neck as a sort of "hello there." This could be compared to you nodding a greeting to a stranger at first meeting. Cats produce cheek pheromones that signal friendship, so sniffing this area can actually help calm feelings of aggression or fear.
Once they feel comfortable with each other the cats progress to sniffing flanks. That could be similar to a human "nice to meet you" polite handshake. This is the area that holds family scent of other cat's body rubs, grooming, or a human's petting hand so it tells the sniff-er quite a lot about the cat.
Cat Butt Presentation
Finally the last step is a sniff of the anal region beneath the raised tail. The cat's signature scent is found here. Kitties that keep the tail down and don't want to be sniffed might be compared to a shy person hiding her face.
A raised tail signals "I mean no threat." So the combination of raised tail with offering a butt-sniffing opportunity is the equivalent of a human's enthusiastic hug or a kiss on each cheek in greeting.
When kitty presents his tail in your face, does he really expect you to sniff? Probably not. Cats are smart, and as much as they love us, they realize we are not feline. But the body language of politely opening themselves up to a sniff-figuratively uncovering their face so we see and recognize the "real kitty"-is a huge compliment granted between trusting friends. The cat butt sniff offer is a back-handed feline compliment.