Because they control the levers which make the financial aspects of the economy run.

The most obvious way is that financial institutions match the funds of investors with capitalization that allows the acquisition of productive assets. This applies to firms and individuals. For example, a bunch of savers, collectively, deposit $10,000 in a bank. Under current reserve requirements of 10% in USA, the bank need only keep $1,000 of that in cash and can loan out the rest. $9,000 is now available to loan to a business to get a secondhand delivery vehicle. That delivery vehicle brings more customers and more revenue from the convenience of delivery. A job is added, in the form of a delivery driver. If you take the added revenue of the firm and the driver and they deposit in the bank, then 90% of those deposits go on loan to repeat the cycle. Eventually, 10 times the amount of the deposit (the inverse of the reserve ratio) is borne from the "multiplier" of money in the economy. In such fashion, loans to businesses can enable acquisition of machinery or facilities to create more production and therefore more wealth. When loans go to consumers, such as for cars, a car adds opportunity to seek work that would be unavailable without transportation. When for a house, that supports housing construction and secondary markets in home maintenance products and services. When the most ignorant of politicians speak of an elevated savings rate as somehow keeping money "out of the economy" they are being, obviously, ignorant. Saved money goes to work, just in a different and more long-term oriented way than consumer-spent money. The only way money gets pulled out of the economy is when little old ladies stash the cash under the mattress, and perhaps even that would be spent eventually.