The degree to which the 'literary' - metaphor, fictions, figurative language etc - inhabits and is necessary to philosophy is a question which Deleuze keeps returning to. The 'conceptual personae' is one response to this question.
To formulate the Cogito, the famous "I think therefore I am", Descartes needs the persona of the Idiot. The Idiot though, is pre-philosophical, or rather pre-conceptual in the sense that he is the prior condition of the concept. He prepares for philosophy proper. The Idiot, innocent or unlearned, disturbs the field of 'received wisdom'. The Idiot requires that we have to explain everything anew, from scratch, so that the world be available to the Idiot, who knows nothing, who lives without the overlay of learning. And in doing this, in having to meet the Idiot on his level, the gaps in in 'what everyone knows' are revealed. We can no longer get round them. Suddenly we are stumbling and stuttering. The encounter with the Idiot makes us relearn how to think. The figure of the Idiot thus prepares the ground for this new thinking but also entails a new implicit picture of what thinking is. Deleuze's point is that every great conceptual innovation drags in its wake a new image of what thinking actually consists in. So it's not that thinking is an underlying constant that generates ever new concepts. In a way, the new concepts generate the thinking.
The conceptual persona can be explicit but often implicit. That is, the philosopher may make visible, as a fleshed out character, the persona who enables a certain kind of thinking. Nietzsche's Zarathustra is an obvious example. But not necessarily, the Cartesian Idiot is an enabling fictional position from which Descartes speaks without being directly visible. "'I think as Idiot"' (Deleuze). It as a mask but it is not Descartes in disguise. In fact, Descartes must supress himself in order to enter the mask and start thinking anew. The mask engenders the thinker.
life is something altogether different from what it is for ordinary people. Above all, things such as money, the stock market, foreign exchange or a typewriter are utterly miraculous (as indeed they are, only not to the rest of us). . . . Is his work at the office, for instance, anything like an ordinary job? To him the office, including his own part in it, is as mysterious and wonderful as a locomotive is to a small child. Have you ever been to the post office with him? Watched him compose a telegram, shake his head while he picks a window he likes best and then, without the least notion of why and wherefore, starts wandering about from one window to the next? . . . No, this entire world is and remains a mystery to him, an enigmatic myth.But once again, as in Descartes, this figure of the idiot is enabling, generating something new, something radical - in Kafka's case a new kind of fiction, a new beam, in light of which the world is transfigured, but also, for him personally, a kind of elective abstention from the world.