Final answer:
Apocrine glands, located in the armpits and genital regions, are the sweat glands responsible for producing the odorous secretions associated with body odor.
Step-by-step explanation:
The sweat glands that communicate with hair follicles in the armpits and produce an odorous secretion are apocrine glands. In contrast to eccrine glands, which are present throughout the body and excrete a mostly water-based sweat, apocrine glands are larger, found in areas such as the armpits and genital regions, and produce a sweat that contains fatty secretions. This apocrine sweat is broken down by bacteria on the skin, which is what leads to body odor. Unlike apocrine and eccrine glands, sebaceous glands produce sebum, not sweat, and are not responsible for the odorous secretion typically associated with sweating.