What does a purely imaginary eigen value really tell us about dynamical system

Question

So I know that in regard to dynamical systems,

if we compute our Jacobian matrix, then to use that to assess stability , we need $\lambda$ to be a hyperbolic fixed point , ie Re($\lambda$) $\neq 0$

What can we say when the eigen values are purely imaginary?

I was told something along the lines of , the stability will look like an ellipse, but I am not sure why or how.