To understand what "marginally bound geodesics" are, you can gain some intuition by thinking about Newtonian gravity. In the newtonian two-body problem, the energy parameter of the orbits dictate whether they're bound or not. If $E<0$, then the orbit is an ellipse (therefore bound) while if $E>0$ the orbit is an hyperbola (unbound). The case separating the two ($E=0$, parabola) would be the "newtonian marginally bound orbit".
In many GR problems we can define a similar "energy parameter". In order to call an orbit bound, we also require the orbit to remain bound under small perturbations (therefore a circular orbit can be unbound, because it might escape to infinity when perturbed). In this sense, consider circular orbits in the Kerr metric (notation as here p. 21-22). Circular orbits can be shown to be bound if the energy parameter satisfies $E<1$, and unbound if $E>1$. The orbits with $E=1$ are therefore called "marginally bound". The reason why in GR you have $E=1$ rather than $E=0$ is that $E$ can be thought of as "energy per unit mass" in units with $c=1$, so that you always have energy due to rest mass. In fact in this case $E\to 1$ at infinity, so the "binding energy" would be $E-1$, which behaves like in the newtonian case. In any case, I don't think the concept is particularly useful, but that's just my opinion.
As to the other question, there's no need for the geodesics to be marginally bound to have a congruence. In fact, there's no requirement that the curves even be geodesics. Generally speaking, a congruence of curves is the set of integral curves of a vector field.