Why are they called "marionettes"?
The most widely accepted etymology is French: marionnette is a diminutive of Marion, which in turn is a diminutive of Marie. The word that now denotes a string puppet literally means something like "little Mary".
The religious explanation
The most repeated — and most plausible — hypothesis links the name to the small images of the Virgin Mary used in medieval religious theatre. Before it became fairground entertainment, the moving figure served the church: it staged biblical episodes and the lives of saints for largely illiterate audiences, where a moving image teaches better than a sermon. The affectionate diminutive is thought to have migrated from the sacred image to the object in general.
A point of usage
It is worth noting how unevenly the terminology travels. In English, puppet is the umbrella term and marionette refers specifically to the string puppet. In French, marionnette works as the general term. In Portuguese, marionete is the string puppet and fantoche the glove puppet, though everyday usage blurs them. Much of the confusion in translated texts comes from exactly this mismatch.
And the figurative sense?
The political use of the word — calling someone another's "puppet" — is much later and exploits the obvious metaphor: whoever holds the strings holds the command. Curiously, the metaphor was already in Plato long before the word existed: in the Laws he describes the human being as a puppet pulled by divine cords, with the passions competing for control. Heinrich von Kleist would invert that reading in 1810, arguing that the marionette is more graceful than the human precisely because it has no self-consciousness.
Other terms of the trade are explained in the glossary.