If an event is said to occur in Outer Mongolia, it quite often means it happens somewhere obscure and hard to find.
If a person is "sent to Outer Mongolia", it means they are effectively relieved of all real power and influence and given a symbolically important but practically meaningless post.
The term refers to the state of Mongolia (in east Asia), a sparsely populated and geopolitically insignificant country inbetween China and Russia. It had a revolution in the early 1920s and effectively became a Soviet satellite state, while never actually being incorporated into the USSR (a model of the later policy in eastern Europe). Although officially designated "Mongolia", it is sometimes called Outer Mongolia because a region known as Inner Mongolia is part of the state of China.
The term gained its present uses because the Soviet foreign minister Molotov, after being relieved of his duties, was appointed as ambassador to Mongolia. This was a pointless role because, being a puppet state and politically insignificant, there were no problematic issues for a diplomat in Mongolia to take care of. In effect, Molotov was sacked but without losing his status or perks; he was simply taken away from the centre of power. This happened in the early years of the Khrushchev regime, soon after the death of Stalin, because Molotov and several others had lost out in bids to become General Secretary (i.e. top dog). Rather than have his rivals shot once they were defeated, Khrushchev adopted the policy of shunting them off into useless and powerless but well-paid posts (another rival, Malenkov, was made head of a factory in Siberia).
(By the way, yes Molotov did invent the "cocktail" which bears his name - he was responsible for mass-producing them in lemonade factories during World War II).
Clare Short was sent to Outer Mongolia in the Cabinet reshuffle, being sent to the Department for Overseas Aid.
I can't believe they put this lecture in Outer Mongolia (i.e. on the far side of the campus from the usual venue).