How do investments and financial markets affect the economy?

Finantial markets  work  as a mechanism of efficient resource allocation.  They drive individual savings into productive economy, by lending funds from savers to borrowers ( who usually are individuals or firms  that  have a business oportunity to develop). Investments, which can be channel through finantial markets, increase the output of an economy, because the pull up aggregate demand by increasing the demand of products needed to expand  firms' production. Therefore, they increase economic product.

Generally speaking, finantial markets help to develop economies, if they are properly regulated, by increasing business activity and investment, hence, the final product into an economy.  

As an example, think of the case of  a family that is saving money to pay their child future education, by buying stocks in finantial markets. If these stocks increase the funds of an specific business, this business has more money to expand its activities, to grow. Therefore, the firm will grow because of the availability of funds to invest, and the family will be able to profit the benefits of the firm's expansion, and to pay their child education in the future.