Private withdrawals simply mean taking money from a business account for personal use. Private withdrawals are not expenses for the financial year, and they are not recorded in your bookkeeping, so they do not affect the business's taxable business income. The business pays tax based on its business income, not on private withdrawals.
A trade name entrepreneur is not an independent taxpayer in the same way as, for example, a limited liability company is. This means that when you earn something with your trade name business, this money is your personal funds, but you still have to pay tax on it. Since the money is in practice your personal funds, the trade name does not have to pay itself a salary, but simply takes the "salary" as private withdrawals from the account used by the company. However, remember that as an entrepreneur you are responsible for paying taxes yourself - so remember to set aside the necessary amount of money to pay taxes.