Organs of action are called karmendriyas in the scriptures. karmendriyas are indriyas(organs) that do karma (action). They are generally five in number: mouth, hands, legs, reproductory organ, and excretory organs.
I am quoting a verse from Srimad Baghavatham that contains the relevant information
The ten senses are the organs of [perception of] hearing, touching,
seeing, tasting and smelling, with the [organs of action known as
the] mouth, the hands, the legs, the genitals and the organs of
excretion as the tenth.
[13, 26, 3, Srimad Baghavatham ]
You can observe that mouth is used for speaking, legs are used for moving, hands are used for various tasks, etc.,
You can read this answer for more general information regarding indriyas.