indirect bandgap semiconductor:
semiconductor in which bottom of the conduction band does not occur at k=0 at which top of the valence band occur; energy released during electron recombination with a hole is converted primarily into phonon; e.g. Si, Ge, GaP.
(Phonon: A quasiparticle which is a quantized sound wave.)
direct bandgap semiconductor:
semiconductor in which the bottom of the conduction band and the top of the valence band occur at the
momentum k=0; energy released during band-to-band electron recombination with a hole is converted primarily into radiation (radiant recombination) wavelength of which is determined by the energy gap; e.g. GaAs, InP.
So, give the semiconductor some energy and if it makes light-it's direct. If you measure the wavelength/frequency of the light, you can get the energy gap of a direct bandgap semiconductor.
I don't think an indirect bandgap semiconductor will produce light, or at least much less than a direct bandgap semiconductor.
P.S. Direct bandgap semiconductors are sometimes reffered to as "optically active" and indirect as "optically inactive".