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I used this link: http://www.oxfordlearnersdictionaries.com/definition/english/engagement?q=engagement
"Given the policy weight these days being placed on central banks' shoulders, and the changing social and technological landscape facing them, it is probably as good a time as any to begin exploring these new frontiers of central bank engagement," he told a conference at the Federal Reserve Bank of San Francisco.
Source: http://www.reuters.com/article/us-britain-boe-haldane-idUSKBN1722V6?il=0
The abstract noun engagement is formed from the verb engage. This meaning here is similar to that in "to engage someone in conversation", that is, to speak to them in order to establish communication between them and yourself.
Engagement could be defined as "Modes of communication with a target audience". The article is about how banks communicate with the general public.
A company may have an "engagement strategy", a plan for getting its "message" out to a target audience. It would be synonymous with a "public relations" strategy.
At its core, you can consider 'engage' to mean 'to connect', and it underlies all the other definitions which have greater or lesser degrees of abstraction because in each case, some sort of connection is being made. Whether 'connecting' with an audience, or 'connecting' with an activity (as in 'engaged in thievery') or engaging to be married (connecting in a pledge to be married) or in the original example context, the bank's 'engagement' with other entities, such as customers, governments, etc. Originally it referred to entering into a pledge or promise (a brief overview is at Dictionary.com's 'engage' definition)
While etymology doesn't constrain a word's meaning, it can often help to get some perspective on the nuances of its meaning.
