Why did we evolve to be able to see this specific set of wavelengths only?
Well humans actually have a reduced spectrum compared to non-mammals. Reptiles and birds have 4 color sensitive cell types (cones), mammals lost two of these as modern mammals are descended from early mammals who were nocturnal. Primates evolved a third cone, (a mutant variant of one of the two they had before) Primates did this because many a frugivores and color is excellent for determining when fruit is ripe.