When you perform resistance exercises, you cause microscopic tears within your muscles. Your body responds to this trauma by repairing the muscles which grow stronger. While you can do a full body workout every day, you won't give your muscles enough time to recover and you risk injuring them instead of building them.
The American College of Sports Medicine tells novices to do two to three full body workouts per week with at least one rest day between them. The recommendation for intermediate individuals is to do three workouts per week, again with at least one rest day between workouts. The ACSM doesn't recommend full body workouts for advanced individuals. Those people should do four to six days of workouts split into upper and lower body routines.
Depending on the level of your workouts you may need more than one rest day between workouts. According to Jonathan N. Mike, M.S. and Len Kravitz, Ph.D. of the University of New Mexico, exercises with greater muscle recruitment, like the deadlift, squat and overhead press, require more rest. Mike and Kravitz recommend one to two days rest between sessions.