They've applied a 3D transform to the slides in a keyframe animation, so when you click on next/prev a rotateY(..) with a translateX(..) gets applied to the slide which moves the slides while creating a 3D box like effect.
it's quite complex so you'd have to put in some time to do it smoothly, you can try following their animations code from here techcube.pk/templates/template20/css/animations.css
hope it helps! :)