The most elegant way I've seen to describe this is described in the paper The river model of black holes. If we write the Schwarzschild metric in Gullstrand-Painlevé coordinates we get (in units where $c = G = 1$):
$$ ds^2 = -dt_{ff}^2 + \left(dr + \beta dt_{ff} \right)^2 + r^2 d\Omega^2 $$
where:
$$ \beta = \sqrt{\frac{2M}{r}} $$
This looks like the Minkowski metric except that the radial coordinate is replaced by $dr + \beta dt_{ff}$. The parameter $\beta$ has the dimensions of velocity, and in fact it's equal to the Newtonian escape velocity. $\beta < 1$ outside the event horizon, $\beta = 1$ at the event horizon and $\beta > 1$ inside the event horizon.
The physical interpretation of this is that the radial coordinate is flowing inwards at a velocity of $\beta$. In effect space is flowing inwards into the black hole and carries observers along with it in the same way a river carries along observers floating on it - hence the name river model. A light beam moves with velocity $1$ with respect to the spacetime around it, so relative to the observer at infinity the net velocity of a radial outbound light beam is:
$$ v_{eff} = 1 - \beta $$
So outside the event horizon $v_{eff} > 0$ and the light beam moves outwards. At the event horizon $v_{eff} = 0$ and the light beam is frozen at the horizon unable to move outwards. Inside the event horizon $v_{eff} < 0$ i.e. even if you shine the light directly outwards it still moves inwards towards the singularity.
As it happens I have addressed this issue before, in the question Why is a black hole black?. However that was a more algebraic approach and I think the river model approach is far more intuitive (insofar as anything in GR can be intuitive!).