Lower interest rates help the stock market by increasing the money supply. The larger the money supply is, the more money there is available to invest in the stock market.
Lower interest rates allow companies to borrow at lower rates and thus provide higher returns to shareholders. They also force investors seeking higher returns to buy stocks.
Businesses use borrowed money to buy inventory to be sold and to expand and improve their operations. Low interest rates allow businesses to lower the costs associated with this borrowing.