According to a WP article "Some call Trump a Manchurian candidate",
The comparison to Trump is derived from the thought that he might be a puppet of the Russian government.
The phrase first came into existence thanks to Richard Condon, who in 1959 wrote a novel by that title — “The Manchurian Candidate” — in which a platoon of decorated soldiers return from the Korean War, after being brainwashed to believe in communism. One of them has unwittingly become a sleeper agent, controlled by the communist Chinese and Soviet governments to perform a particular assassination, which will allow them to install a communist puppet dictator as U.S. president.
It's also explained in TVTropes as Manchurian Agent
A person is Brainwashed so that, on a certain trigger (either a situation, or else a phrase only someone in the know would ever say), they will go from their normal self to The Mole; they will most often remember nothing afterward. Occasionally, they can be programmed to do even more serious crimes, such as attacking their teammates outright, but their true value lies in the fact that their cover is so deep that not even they realise it.