A parabolic fixpoint is a fixpoint $p$ of a function $f$ such that $f'(p)=1$.
In some literature also a fixpoint $p$ with $f'(p)=e^{2\pi i q}$, $q\in \Q$ is called parabolic, because there is some $m\in\Z$ such that $(f^m)'(p)=1$ (remember $(f^m)'(p)=f'(p)^m=e^{2\pi i qm}$).