"Allied health" refers to a wide range of health professionals, excluding physicians. The term encompasses occupations such as clinical lab technicians, emergency medical technicians (EMTs), occupational therapists, physical therapists, medical assistants, physician's assistants, health physicists, and other medical technicians.
Many of these occupations require a specialized 4-year undergraduate degree; some, like physician's assistants, may need a master's degree. Some people consider nurses to fall in this category; others categorize them separately.
The information in this writeup was taken from the science dictionary at http://biotech.icmb.utexas.edu/; I oversaw the development of the dictionary (the website was mothballed in 1998) and I believe I wrote the entry this is based on.