A curve ,let's say $(x(t),y(t))$ is said to be smooth if $x'(t)$ and $y'(t)$ both exist and are continuous.(Am I not right?)  

A function differentiable at a point intuitively means that its graph on coordinate plane has a unique tangent(no corner) at that point.  

So what does a smooth curve mean intuitively ?   

Thanks in advance!