If a company needs money, it can either borrow or get investors. For the former, the company pays interest to a bank, deducts the interest payments from its taxes, and the bank pays taxes on its profits: The money is taxed once. For the latter, the company pays dividends to the investors, pays taxes on the money given to investors, and the investors pay taxes on that money again: The money is taxed twice.
While I would argue that allowing businesses to write off dividends would be the more direct approach, eliminating the personal tax on dividends is a step in the right direction. If the double tax is removed from dividends, it will encourage investing and encourage companies to carry less debt.
The sudden surge in the market when the proposal was announced should be enough evidence that this would help our economy. Sometimes the government has to help the rich so everybody else can benefit too.
