Attracting fixed point

A fixed point $p$ is attracting (or a sink) if $\exists ϵ>0:\forall x\in N_{ϵ}(p)$, ${\lim }_{k\to \infty }{f}^k(x)=p$.

In plain English, nearby points converge to $p$ under iteration.

A period 2 sink would be two points $p_1$ and $p_2$ such that $f(p_1)=p_2$ and $f(p_2)=p_1$, and nearby points would oscillate between converging to $p_1$ and $p_2$.