Earlier quoted context omitted.
OK but what can they do with this balance
Settle payments with other banks is the obvious one - when you send money from Wells Fargo to Chase for example, they settle it behind the scenes by asking the fed to increase Wells balance and decrease Chase's. They can also use it to buy securities from the Fed, to buy securities from other banks, to settle derivatives contracts and margin calls around them.
how does this make its way into stocks