notation on MO diagrams
There is likely a question that addresses this on the site already, but I couldn't find it either, so I'll add an answer here. 

You are correct that these symbols relate to the symmetry of the molecular orbitals that they label. In chemistry, we often label molecules by their point group symmetry, which describes how the molecule behaves with respect to particular symmetry operations (e.g. rotations, reflections, inversions).

If a molecule has a particular point group symmetry, its orbitals (and some other properties like vibrations) can be divided up into irreducible representations, which are essentially just different ways in which the overall symmetry can occur. One can find these irreducible representations (often shortened to irreps) in a character table for that point group. 

$\sigma_\mathrm{g},\sigma_\mathrm{u},\pi_\mathrm{g},\pi_\mathrm{u}$ are all irreps of the $D_{\infty\mathrm{h}}$ point group, which you will most commonly encounter as the symmetry of a homonuclear diatomic. Since you are just being introduced to these, you won't likely use a character table and will just be given these MO diagrams. 

At the level you will need for the moment, $\sigma$ orbitals come from the overlap of a single lobe from each atomic orbital and $\pi$ orbitals come the overlap of two lobes from each atomic orbital. The $\mathrm{g}$ and $\mathrm{u}$ labels tell you whether the orbital is symmetric or antisymmetric under inversion, that is, if you move every point $(x,y,z)$ to $(-x,-y,-z)$, does the sign of the orbital remain the same or does it become the opposite sign. The * label is used to describe whether an orbital is bonding (overlap is between atomic orbitals/lobes of the same sign) or antibonding (overlap is between atomic orbitals/lobes of opposite sign).