Huckel's 4n+2 rule is used to determine if a planar, cyclic, conjugated system has aromatic character or stabilization. A molecule is typically considered aromatic if it planar, cyclic, conjugated and has 4n+2 π electrons where n=0, 1, 2, 3 etc.
For example benzene which is planar, cyclic, conjugated and has 4n+2=6 π electrons (i.e. n=1) and therefore is aromatic.
Recall from the discussion of Frosts Circle Mnemonic that we can easily construct the MO energy levels of a cyclic conjugated system by placing the polygon (hexagon for benzene) such that one corner is pointing down. Below is the MO energy diagram for benzene. As long as at least one energy level is completely full then the system is stable or aromatic. The lowest energy level can only ever hold a maximum of two electrons (ψ1), while the degenerate ψ2 and ψ3 can hold a maximum of 4 electrons. Therefore in order to be aromatic there must be 4n+2 π electrons.