Symbolism, Imagery, Allegory
Are There No Strings on Him?
As an admirer of Stoic philosophy, Marcus is all about having a peaceful mind that's indifferent to all things of the flesh: pain, pleasure, emotional response. What he prizes above all things is self-restraint and self-discipline, as well as total self-sufficiency. Marcus doesn't want to rely on anything external for fulfillment.
But this kind of independence isn't easy to achieve. Marcus continually warns himself to be aware when he's not being governed by his "directing mind": "... don't let this directing mind of yours be enslaved any longer—no more jerking to the strings of selfish impulse" (2.2).
While Marcus never tells us specifically what kind of naughty behavior he might be indulging in to bring on the puppet-strings comparison, it's clear that he's not pleased at his failure to become a real boy.
To be subject to impulses—responses that come from sensual experience—is to degrade his rational mind, since a "... response to the puppet strings of impulse is shared with wild beasts..." (3.16).
Tangled Up
It's clearly a constant battle for Marcus to retreat into his mind far enough to avoid the impulses that pull him away from his philosophical principles. By Book 12 (which was written toward the end of his life), Marcus is still struggling to break free of his strings and gain the autonomy he knows he should have by now:
Realize at long last that you have within you something stronger and more numinous than those agents of emotion which make you a mere puppet on their strings. (12.19)
Get a load of the weariness in the emperor's tone here. It seems that for some good practices, things are easier said than done.