In short
Stem cell exhaustion is the age-related decline in the number and regenerative function of adult tissue stem cells, reducing the body's capacity to repair and replace damaged tissue.
Adult stem cells reside in specific tissues (bone marrow, muscle, gut lining, and others) in limited numbers, dividing occasionally to replace lost or damaged cells while otherwise remaining in a quiescent, undifferentiated state. Over a lifetime, this population accumulates DNA damage, its niche (the surrounding supportive tissue microenvironment) degrades, and a growing fraction of stem cells become senescent or lose their capacity to differentiate properly.
This is well documented in hematopoietic stem cells (which give rise to blood and immune cells): aged hematopoietic stem cells show reduced regenerative capacity and a skewed output toward myeloid cells, contributing to the immune aging seen in older adults. Muscle satellite cells (the stem cells responsible for muscle repair) similarly decline in number and function with age, contributing to sarcopenia.
This is one of the mechanistic hallmarks cited to justify interest in stem cell therapies for aging and tissue repair, but it is important to separate the biology from the therapy: stem cell exhaustion describes a well-documented decline in a person's own endogenous stem cell pool, while stem cell therapy (injecting cultured donor or autologous cells) is a distinct, much less established intervention with its own separate — and currently limited — evidence base for general anti-aging use.