Why is the Federal Fund rate so important to investors? shouldn't this only affect the rate at which banks can lend to each other/ with the Central Bank?

You are right, the rate applies to interbank borrowing. But it does have spillover effects to the economy at large.

If fed rate increases, it becomes more attractive for banks to lend/deposit with the central bank. Hence, lesser funds are available to loan out to public. To make it more attractive for banks to lend out to consumers/businesses, loan rates will have to increase. Another spillover for this is that for banks and companies to get more funds from the public, they will naturally increase interest rate/bond coupons rate.

The opposite will occur when fed rate reduces; banks will choose to lend more funds to the public, lowering loan rates to attract more lenders and deposit rates since they do not need that much funds.

The economy consists of transactions -all the spending happening. Spending = credit + money supply. The Fed controls both to keep the economy growing at the right pace and keep inflation at 2 to 4%. When the Fed wants people to spend more, they increase credit by reducing interest rates -make borrowing and spending attractive. When they want people to spend less, or control inflation they increase rates and make borrowing expensive. Sometimes, manipulating credit is not enough, so what you saw after 2008 was printing of money to increase spending. From an investor's perspective, all asset returns are relative to cash..hence when cash returns go up, other assets have to increase their return to continue been attractive enough. This happens by reduction in price of the asset(eg.bond prices go down to increase yield).
Hope that clarifies..