Chapter 13 is the reorganization bankruptcy because it allows the debtor to reorganize their finances in such a fashion that their creditors get paid, even if only a little bit.  It is similar to the Chapter 11 reorganization that is used by Donald Trump or other big businesses, but it is geared for the little guy.
Essentially, Congress said that if you make ‘too much money’ (as in you ‘fail’ the means test) and you don’t qualify for one of the few, highly specific exceptions to the means test, then you have the ability to pay back some of your debts, and you should do so, for a period of 3 – 5 years, depending on your income.
Now, there is nothing that says you can be forced into a Chapter 13 bankruptcy… thankfully slavery is utterly and completely prohibited in this country now, but if you (1) need to file for bankruptcy protection for whatever reason, and (2) you don’t qualify for Chapter 7 relief, then a Chapter 13 is most likely the only way to go.
Being ‘in’ a Chapter 13 means being in a 3 – 5 year payment plan, where you have to adhere to a reasonable budget and make monthly payments to the bankrupcy trustee.  The amount of the monthly payment is determined by your disposable monthly income (essentially, this is calculated by taking your net monthly income minus your monthly expenses).
The trustee then makes payments to your creditors in order of priority.  For example, if you owe the IRS a small amount of money, they will be the first ones paid by the trustee.  There are a number of levels of priority, and essentially credit cards and other unsecured creditors are at the very bottom of the totem pole.  Some debts (the ones with the high priority, must get paid through the plan, and the rest of the debts are discharged upon completion of your plan period.