In daily life we are using semiconductor devices. LED are one of them whom we are using in TV remote, traffic signals etc. The materials required to make those devices are direct band gap material.
Indirect Band gap material: During recombination if electron from conduction band is not coming to hole location directly then that is indirect band gap material. Basically electron is coming from conduction band to valance band via trapped energy states. These energy states make some momentum of electron and hole to make recombination possible.
Direct Band gap: During recombination process, electron will directly come from conduction band to valance band without changing momentum and without any trapped energy states. This type of devices are known as direct band gap material.