Welcome to the forum Alex.
He is talking about it in terms one might use about a journey by train, bus, or plane.
For example I might say to someone, "I take the 07:30 train to Swansea, where I change [trains] to catch the train to London".
In this context, the train / plane / bus you are trying to catch is known as "the connection". Hence the reference to "the connection with boredom".
E.g. "We'd better hurry up or we'll miss our connection", might be heard on a railway platform as two people hurry past having got off one train while they are rushing to catch their next one.
Usage A2 Verb (Transport): http://dictionary.cambridge.org/dict...british/change
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