These are so-called irreproduciple representations (sometimes just called irreps) from group theory.

A1g is a non-degenerate total-symmetric vibration, that means it is symmetric under all symmetry operations (rotation, mirror plane, inversion center).

E12g is a double-degenerate vibration that is symmetric under inversion (that's the g).

Regarding the specific shapes of the vibrations I can't say more, MoS2 is not my material system.

In short, they are irreducible representations (see group theory for more detail), E12g is in-plane vibrational mode and A1g is out-of-plane vibrational mode. An example of what information they can tell you that, if MoS2 (1L or 2L) is under strain, there will be shifted (or splitted) with E12g mode while A1g mode is maintained.

see https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Group_Theory/Understanding_Character_Tables_of_Symmetry_Groups

Every molecule has a point group associated with it, which are assigned by a set for rules (explained by Group theory). The character tables takes the point group and represents all of the symmetry that the molecule has.

for more detail, See below link

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Group_Theory/Understanding_Character_Tables_of_Symmetry_Groups

Raman Spectroscopy provides insight into the signature bonding and associated emission to vibration modes with these bonds. In the case of MoS2 monolayers - the inplane E12g peak is observed at 384 cm-1, and out of plane A2g peak is at 404 cm-1. The delta = 20 cm-1 between these two peaks is the signature for monolayer MoS2. For an increase in the thickness of MoS2 deposition, there is an increase in the delta; that is the two peaks move apart.