If we plot the E-k Diagram of any material, we will get the Valency and Conduction band shapes for every k (K is the wave number which is directly proportional to momentum and E is the total Energy).
If we define the energy band gap as the distance between the maximum point of the Valency band(VB) and the minimum point of the Conduction band(CB), we have one of two cases:
1. The max of the VB is directly under the min of the CB: This is called a direct badn gap material.
2. The max of the VB is not directly under the min of the CB: This is called an indirect band gap material.