Financially, leverage is the ability to control an asset with cash equal to less than the full cost. This means that you borrow to purchase the asset. The goal is to increase the rate of return from an investment.
When you buy stocks on margin or get a mortgage on a piece of real property, you are leveraging a small amount of your own money to control greater valued assets. These leveraged purchases allow you to retain all of the capital gains on a large purchase.
In real estate investment, it is routine to purchase a property -- even an investment property, with only ten percent down. If you do this only when you are sure that the income generated by the property will cover the payments on the note, over time, then you have realized all gains of equity through payment and appreciation by investing only one tenth of the cost of the property. From a cashflow perspective this is fantastic.
You can understand the analogy between financial and mechanical leverage by considering the fulcrum to be the divider between the chunk of the investment funded by you and the (hopefully much larger) chunk provided by your banker. The further over that fulcrum is (minimizing the percentage that you must invest) the more leverage you are getting on the investment.
And the worse things can go for you if you've gotten in over your head and ignored or failed due diligence.