A curve cast is a handy way to work around obstacles or tuck a fly right along the bank.
Basically, you stop the rod abruptly with the rod at an angle, and instead of tracking straight (up and down) the leader kicks either right or left, depending on which side you’re powering the stroke from.
My favorite way to do it, however, involves a twist. I like to make my normal casting stroke, and then at the end as I am stopping the rod, I cock the rod so the reel ends up parallel to the water surface, instead of hanging straight down. It isn’t an overly aggressive move; it’s more turning the knob on a stove to light the burner. A simple flick of the wrist as the rod tip stops will send that leader and fly off to the side.
Of course, if you don’t want the fly to land sideways and it does, maybe you’re cocking the wrist without realizing it. Pay attention to where your reel is as you cast, and that will help you go straighter, or make curves on purpose. Practice a bit and you’ll feel it.