bandgap has an importance role for conduction.if bandgap is max,the conduction of electron is min. and vice-versa.hence we can say that the bandgap desides the conductivity of any material(may be metal or nonmetal)

Optical bandgap means bandgap estimated using optical means or characterization. In simple words, let a light of different energies incident on the material. The material absorbs some energies and transmits some energies (the detector measures this). The threshold energy at which the material starts absorbing light is "Optical Bandgap".

In a similar manner, electrical bandgap means bandgap estimated using electrical means or characterization. Here instead of measuring what light is observed of transmitted. You make electrical contacts for the material and measure the current instead of optical absorption. The incident light is of course absorbed, and carriers (electrons and holes) are generated in proportion to absorption. We measure current (nothing but charge which is proportional to absorption) and this current too shoots up at a threshold energy i.e. electrical bandgap.

Bandgap

becoz Si and Ge are indirect bandgap semiconductors. for lasing action direct bandgap semiconductors are required of the type In Ga As P