An E2 elimination occurs when a proton adjacent to a leaving group is extracted by a base with simultaneous elimination of a leaving group and generation of a double bond.
Similar to the relationship between E1 eliminations and S1 mechanisms, E2 eliminations often occur in competition with S2 reactions.  This observation is most often noted when the base is also a nucleophile.  In order to minimize this competition, non-nucleophilic bases are commonly used to effect E2 eliminations.
E2 eliminations proceed through initial extraction of a proton by a base or nucleophile leading to Elimination of a leaving group justifying the E designation.  Because this mechanism proceeds through the interaction of two species (substrate and base/nucleophile), E2 reactions are recognized as bi-molecular.  Thus, the involvement of 2 species in the initial phase of the reaction enhances the mechanistic designation to E2.