The primary function of the mitochondria in eukaryotic cells is to produce adenosine triphosphate (ATP), the main energy currency of the cell. Mitochondria convert biochemical energy from organic compounds into ATP through a process called cellular respiration. This energy is vital for various cellular processes and overall cell function. Additionally, mitochondria are involved in regulating cellular metabolism, apoptosis, and storing calcium ions, playing a pivotal role in cellular health and energy management.