You can see Stoic Philosophy of Mind:
The Greek concept of the soul is much broader and more closely connected to basic bodily functions. The soul is first and foremost the principle of life; it is that which animates the body.
The Stoics argued that the soul is a bodily (corporeal) substance. Although the soul is a body, it is best to avoid calling Stoic psychology materialist. The Stoics contrasted soul and matter. For this reason scholars generally prefer to call Stoic psychology corporealist, physicalist, or vitalist.
The idea of sensation as the transmission of sensory information is illustrated in the final two analogies of the soul. [...] The second analogy states that the soul is like a spider in a web. When the web is disturbed by an insect the movement is transmitted through vibrations to the spider sitting at the center. The human soul in a like manner extends through the body like a sensory grid establishing a sensory tension. All perceptual information is transmitted by a tensional motion.
Marcus Aurelius' "sympathetic link" is a mechanism of transmission of this sort which establish the communication between body and soul.
See P.A. Brunt, Studies in Stoicism (2013), page 455:
The old Stoics described man as a compund of soul and body. This duality is accepted by Marcus [...]. He recognizes like Cleanthes that there must be interaction (sympatheia) between mind and body, but warns himself not to let his mind become the servant of the body, mastered by sensations of pleasure or pain in the flesh [footnote: Sympatheia, v.26; iv.39].
For Marcus Aurelius' "background" can be useful to see Epictetus.