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If you’re an employee in Germany, you will see the term „Lohnsteuerklasse“ on your paycheck. This is a number that refers to your Tax-Class, based on this your taxes are calculated. Not only the tax rate, but also social insurance and solidarity contributions and church tax are calculated based on this Tax class. Your net salary, as an employee is therefore, based on your tax class. This applies only to employees and not self-employed persons
How to find your Tax Class
Once you arrive in Germany and register yourself (Anmeldung), a tax class is assigned to you by the Finanzamt based on your marital status.
In the German tax system there are a total of six different wage Tax classes, which are based on the family situation of the individual taxpayer. If you already know your tax class, you will receive further information by clicking on the respective button. The table below shows the details of which tax class you could belong to.
STEUERKLASSE - 1

This is the default tax class that is applied to single (unmarried) people; couples who live in a civil partnership (registered) who are divorced, widowed or married. Once married, you should apply for a change of tax class and would automatically be moved to 4&4. Some married couples can be in Classes 3&5. People under this Class pay high Tax in comparison to other Tax category.
IMPORTANT: If you are married and your spouse lives in home country, then you will be still put in the CLASS 1, Germany accepts the tax class change, only when your spouse landed in germany, get registered in the aliens office and applied for the tax class change.
STEUERKLASSE - 2

This tax class is for single parents who live alone with their children and entitled to Kindergeld benefits. Some of them are applicable to other benefits from the government as well.
STEUERKLASSE - 3/5

STEUERKLASSE -3 This tax class is for married couples, when one spouse has no income, lower income than the other or chooses to be in Tax class 5. It also applies to windowed employees for the year of death of the spouse. Read below to understand the benefits of being classified under Classes 3&5. Spouse earning higher than other partner must choose this Tax class.
STEUERKLASSE -5 This is the counterpart to the tax class 3. one can choose this combination, when the other spouse chooses to be in Tax class 3, the other is automatically assigned Tax class 5.
STEUERKLASSE - 4

This is the default tax class for married couples, who have not chosen Classes 3&5. If both the couples earn almost equal amount, then it doesn’t make sense to shift to 3/5 or 5/3 class combination, because you don’t save any amount significantly here. As soon, you get married and registered in einwohnermeldeamt, you will be put to tax class 4, so its your duty to change the tax class, see here to know, how to change the Tax class
STEUERKLASSE - 6

When an employee has a second job and earns more than 450€ per month on this job, he is under Tax Class 6.
Benefits of Tax Class 3&5
If you are married and your spouse lives in Germany, then you can choose different tax classes and reap benefits. This way, you can optimize your tax return. The default tax class for married couples is Class 4 but you can benefit from being assigned Class 3&5.
If one spouse earns significantly higher than the other, it is understood that they are bearing most of the household costs – hence getting a tax rebate for this reason. If you are in this situation, you can move to Tax Class 3 and receive more net salary than being in Class 4.
When one spouse chooses to be in Class 3, the lower earner is automatically assigned Tax Class 5. This situation is the most beneficial when one spouse earns at-least 60% of the total income of the household.
Related Blog
How to Change Tax class in Germany?