Smart guess. "empirically treat" means taking an educated guess. The scenario you describe means there is an infection but it has not been determined which bug causes it. When there is no precise information on the infectious organism, usually two or three antibiotics are chosen and given to the patient "empirically" to see if there is improvement.
Broad spectrum. You have to know what type of bacteria that most like would cause a spinal infection, and the antibiotic that most likely would cover these bacteria(staph aureus , strep pneumoniae, gram negative and possibly anaerobic bacteria), culture should be obtain to identify the specific bacteria that cause the infection then target these bacteria specifically.