Discretionary income is the income that is left over after necessary spending (i.e. taxes, bills, other necessities for running a business). Equity in accounting is how much your particular business/location is worth versus your debts.
Both discretionary income and equity is very important in entrepreneurship because in order to be successful, you need a certain discretionary income left over to make a profit. If you're spending all of your money on your necessities to make your business run, you will "break even", meaning you will not return a profit. This ties into equity. If you're continuing to "break even", your equity will lower. You want your ratio to value of your business and a lower debt to make things balance out in your favor.