What exactly does the Kretschmann scalar implies and how does it work? From the General Relativity class lectures I understood that this particular invariant, the Kretschmann scalar namely
$$R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho}$$
is really important because, through it, we can understand if a certain metric has removable singularities or essential singularities.
Why exactly does it work? 
Am I wrong, or have I understood also that this scalar tells us if we are in presence of a gravitational field? Or was that a Riemann Tensor property?
Are there other important and useful scalar like the Kretschmann one? 
 A: If you discover your metric has a singularity it can be very difficult to work out if this is a real singularity or just an artefact of the coordinate system you've used. If you've just run into a coordinate singularity then you can eliminate it by a coordinate transformation, but there is no easy way to work out what transformation is necessary. If you cannot find a coordinate transformation that eliminates the singularity this doesn't mean the singularity is real - it might be you just haven't stumbled across the required transformation yet.
But suppose you could find a quantity that didn't depend on whatever coordinate system you used i.e. it didn't change as you changed the coordinates. This would be a good way to look for singularities because if your quantity becomes infinite then it must be infinite in all coordinates, and that means the singularity is real.
General relativity has several such quantities, and we generically refer to them as scalars. The simplest is the Ricci scalar, but we are often interested in vacuum solutions and for a vacuum solution the Ricci scalar is zero everywhere so it isn't much use. For example this is the case for Schwarzschild and Kerr black holes.
The Kretschmann scalar is more complicated to compute, but unlike the Ricci scalar it (usually) isn't zero everywhere so it's far more useful. The Kretschmann scalar for a Schwarzschild black hole is given by:
$$ R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho} = \frac{48M^2}{r^6} $$
Since this isn't infinite at the event horizon $r = 2M$ we can tell immediately that the event horizon is a coordinate singularity not a real one. Likewise we can tell immediately that there is a real singularity at $r=0$.
There are a number of these scalars, and the Wikipedia article on curvature invariants lists a few of them.
