A huge benefit of creating a budget and sticking to it is that it forces you to get organized. That organization gives you the ability to track your cash flow and leads to actually being able to free up money.
Month after month as you go through your budget you will start to see areas to free up money by eliminating unnecessary spending habits. You may identify purchases that you make weekly or monthly that you realize if you would just give it up, it would free up $50, $100, or more each month.
By freeing up cash it will allow you to re-allocate money to pay off your credit card debts. Or it might allow you to save for a replacement car. You could start putting that money towards your child's education. And this is the whole purpose for getting out of debt. To free up money that use to go on credit cards. To prevent you from going into debt. A budget is just a tool to achieve this freedom.
And it can happen quickly. Soon after our family got on a budget, my wife's mother was hospitalized. My wife wanted to take a week off to go be with her. This was about the 3rd month into our budgeting experiment. By this point I was very organized with our budget and was already cutting out wasteful spending and targeting money to pay off debts. Had this happened the year before when we were living paycheck-to-paycheck it would have caused much anxiety over the thought of her taking a whole week off from work. But by looking at our budget I realized that the extra money I was freeing up to pay off debt could easily be used as an emergency fund to cover any shortfall by my wife not working. And I quickly realized she could take more time off. I told her, "why don't you go for two weeks." I think she thought I was kidding at first but I showed her on paper how it would be okay and it would not hurt us financially. And it would not even throw our debt repayment that far behind. So she took two weeks off to fly to N.J. to spend time with her mom. This may have been the start of my wife really getting on board with the whole budgeting idea after seeing how well it worked in this unexpected emergency.
Once you have focused your budget to better position yourself to pay off debts and you finally start to erase debt then you can use that money to either pay off more or simply save it. By mapping out where your money will go you can actually free up cash to be used where it is really needed.