It is an interesting question since ALL the semiconductors has direct and indirect transitions. A direct transition is a transition from the valence band to the conduction band without the assistance of phonons; an indirect transition is a transition from the valence band to the conduction band with the assistance of phonons. However, a semiconductor is named "direct" when the probability of a direct transition is higher than an indirect transition.
It is an interesting question since ALL the semiconductors has direct and indirect transitions. A direct transition is a transition from the valence band to the conduction band without the assistance of phonons; an indirect transition is a transition from the valence band to the conduction band with the assistance of phonons. However, a semiconductor is named "direct" when the probability of a direct transition is higher than an indirect transition.
what P. Grima wrote describes almost very good but implicitly the meaning of direct and indirect bandgap. This is the consequence with respect to transitions.
The terms direct or indirect refer to the energy structure E(k) with k as momentum hk in the momentum space. If the valence band maximum at kV and conductivity band minimum at kC are located at the same momentum k you have a direct gap. In the other case (kC - kV >< 0 ) the gap is indirect. In the case of transitions of electrons from conductivity to valence band a phonon effects the momentum exchange.
In a semiconductor after irradiation, photon excites an electron from the highest-energy state in the valence band to the lowest-energy state in the conduction band without changing crystal momentum is known as direct band gap.