They are "deep" in the sense that the energy required to remove an electron or hole from the trap to the valence or conduction band is much larger than the characteristic thermal energy kT, where k is the Boltzmann constant and T is the temperature.
They also directly interfere with the operation of transistors, light-emitting diodes and other electronic and opto-electronic devices, by offering an intermediate state inside the band gap.
Hence, deep-level traps are not appreciated in many opto-electronic devices as it may lead to poor efficiency and reasonably large delay in response.
Common chemical elements that produce deep-level defects in silicon include iron, nickel, copper, gold, and silver.
Surface states and crystallographic defects in the crystal lattice can also play role of deep-level traps.