Annual income of less than 9,744 € is not taxed at all. Income tax starts with 14.00% and gradually goes up to 42.00% (top tax rate applies to taxable income of more than 57,918 €). The amounts double for married couples filing joint returns. As your income goes up, the tax rates go up. This happens without any significant jumps in a way that you would suddenly be in a significantly higher tax bracket. The rates go up in increments of 36 € (a sliding scale concept).
You can work out your German annual income tax liability online at https://www.bmf-steuerrechner.de/index.xhtml. You need to enter your taxable income (“zu versteuerndes Einkommen”) after deducting all expenses.