Red-eared sliders are very common turtles both in nature and in captivity. They live primarily in the water, but because they are cold-blooded, they do emerge to sunbathe in order to modulate their temperature. They live in diverse habitats—from mud holes to ponds, streams, lakes, and large rivers. Red-eared sliders are native to the southern United States, though they are prevalent around the world because they are so popular as pets.
In fact, this turtle is thought to have the highest volume of reproduction worldwide and they are often sold to people as hatchlings. They are probably dumped into the wild both in and out of their native habitat more any other turtle species on the planet.
The fluttering claw movements that red-eared sliders sometimes exhibit is most often a courtship ritual or "mating dance." It is most often males that exhibit this behavior, but not exclusively, so you can't necessarily use this behavior to distinguish between males and females. When some male turtles try to woo females to mate, they approach them underwater and then the turtle will face the other and flutter or vibrate its front claws around the female turtle's head. When the female turtle catches sight of this and is amenable to the invitation, they drop to the aquatic floor. At this point, the pair are ready to mate and fertilize. If a female is put off by all the fluttering, however, she may respond aggressively. Mating takes about 10 to 15 minutes, but turtles can spend another 45 minutes beforehand just fluttering and wooing.
Sometimes young red-eared sliders will shake their claws around in an attempt at a wooing behavior, even though they're not ready to mate. Before maturity the turtle can't breed successfully, but he can practice claw fluttering so he's ready when the time comes.
Instead of fluttering, some turtles take a more gentle approach, using their claws to actually softly stroke the female's face rather than shaking. The male's claws, which are especially long (and noticeably longer than those of the females), are particularly suited to this special caress.
Performing this courtship ritual does not necessarily mean mating will occur, though, and sometimes it is thought to be more of a display of dominance or territorial behavior. Male turtles sometimes flutter their front claws in front of other males to express their higher social status. This is often an indicator that a physical battle is forthcoming during which the turtles might bite each other with their beaks (as they don't have teeth).