Explanation: Claudius, before he became Emperor, was in the court of his most unfortunate nephew, the mad Emperor Caligula. In order to preserve his life, Claudius played up his disabilities and the perception of stupidity which followed. Rome, well, was not the kindest of places, and poor Claudius had a limp, a stutter, and drooled when he was over-agitated. For obvious reasons, this did not make him look particularly impressive to the gravity and dignity-obsessed Romans - but it also made him seem a very unlikely candidate to succeed Caligula, which may have spared him the paranoid Caligula's wrath. It did not, however, spare him Caligula's cruelty - Claudius was the constant target of mockery, jests, and pranks, including the classic "Put slippers on his hands and tickle his nose while he sleeps so he smacks himself" trick.
When the Praetorian Guard, the personal bodyguard of the Emperor/Secret Police Service, assassinated Caligula for calling their commander a cuck one too many times, a Praetorian found Claudius hiding behind a curtain and declared him Emperor. While there is probably some amount of "Let's control this idiot" in the thinking there, Claudius was, when younger, at least somewhat popular (on account that, like many actors and politicians, he recited and made speeches well; he stuttered primarily in conversation), and, so long as he was silent and still, he apparently cut an impressive enough visage.