정신없이 is the adverb form of 정신없다.
정신없다 has many meanings depending upon context
to be busy to the point of confusion
to be scatterbrained because something is exciting, confusing, hectic
to be hyper
to be in a frenzy
to do something without control, with wild abandon
It really depends upon the context. The term is used often. People even feign to be so busy!