A "blow out heat and style" refers to a professional hair styling service where a stylist washes your hair, then uses a blow dryer and various styling tools to dry and shape your hair into a polished, voluminous look, often including techniques to create smooth, frizz-free results, with the specific style depending on your desired outcome (straight, wavy, curly) - essentially, a full "blowout" where the hair is both dried and styled with heat while wet.