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What's an intuitive derivation behind ODO's definition that helps to internalise its meaning:

to leverage = Use borrowed capital for (an investment), expecting the profits made to be greater than the interest payable:

Etymonline relates only to a physical/mechanical 'lever', not this meaning in finance.

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When researching specialist terms, whether law or finance or any other field, you need to use a specialist dictionary. ODO is good, but is by no means specialist. I used the list at OneLook.com and consulted definitions 28–30.

Yourdictionary.com collates a number of definitions of the word leverage, among which are

noun
1. the action of a lever
2. the increased force resulting from this
3. means of accomplishing some purpose

transitive verb
leveraged, leveraging
to speculate in (a business investment) largely through the use of borrowed funds, or credit, with the expectation of earning substantial profits; also, to mortgage (oneself or one's assets) in this way

[Webster's New World College Dictionary]

It's possible to see here how the use of a lever to result in increased force has been expanded into a financial metaphor: the initial "effort" is an amount of borrowed cash, and the resultant "force" is the profit resulting from investing that cash. If it all goes well, then the result will repay the borrowing and deliver a profit.

The metaphor has been extended further to become a measure of the amount of debt, particularly when comparing to a company's assets.

The amount of debt a company has. A highly-leveraged company has a relatively large amount of debt when compared to the level of assets it owns. Although becoming highly leveraged can create significant profits if things go according to plan, it can severely hamper a company that is caught in a slowing market or experiences unanticipated competition.

[Webster's New World Finance and Investment Dictionary]

This progression is documented in the Etymonline entry:

Meaning "power or force of a lever" is from 1827; figurative sense from 1858. The financial sense is attested by 1933, American English; as a verb by 1956.

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  • +1. Thanks. To clarify though, the key para coupling the mechanical and financial is 'It's possible to ... borrowing and deliver a profit.' The dictionary wouldn't explain this, right? Only cognoscenti can connect, and not an amateur like me?
    – user50720
    Commented Oct 25, 2014 at 13:56

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