What is the importance of reciprocal lattice? Reciprocal lattice is the diffraction plot of a crystal. Now with the STM instrument we can get the get the topology of the crystal, so what is the importance of reciprocal lattice or the Brillouin Zone?
 A: You have to realize that STM is a surface technique. This means that you are probing only the surface, which can be dirty or have suffered from reconstruction, or oxidation. Moreover, it will give you rather limited statistics given the relatively small areas that you can probe.
On the other hand, x-rays probe the sample deeper and with better statistics. You also get extra information about the Structure Factor or magnetic structures if you use neutrons. If you go to inelastic x-rays/neutron scattering, you can probe for a myriad of excitations (phonons, magnons, orbitons) that are unlikely to be seen with STM. And all of this information come from techniques (x-rays and neutron) that are inherently linked to the reciprocal space.
Also, it's very helpful when you discuss delocalized states in the crystal, for example conduction electrons in a metal.
Regarding the Brilloin Zone, this is mostly a geometrical tool to better organize the reciprocal space.
Hope this clarifies a bit, and I would say that this is only the tip.
