You might ask yourself why you actually need travel health insurance? Are you not insured abroad by the normal, statutory health insurance? The answer to this question is: Unfortunately only partially!
On one hand, it depends on which country you are traveling to:
If, for example, you are travelling to a country that is not a Schengen country, such as Tunisia or Egypt, you are simply not covered by health insurance without private travel health insurance and are therefore exposed to an extreme health and financial risk. If you need medical treatment there and, in the worst case, even need to stay in hospital for several days, you will have to bear all the costs alone.
Especially in countries where medical and treatment costs are much higher than in Germany, such as in the USA or Canada, expenses can quickly arise that bring a normal earner without travel health insurance in financial distress.
On the other hand, the nature of your illness or the extent of the treatment you require plays a role:
most European countries, i.e. the so-called Schengen states, have a social security agreement with Germany. As long as you stay in these countries, your health insurance will cover the costs of treatment etc.. However, only to the same extent as in Germany: If a treatment abroad costs, for example, 1000 €, but in Germany the same only 800 €, you have to pay the difference out of your own pocket. Unless you have a private travel health insurance, which takes effect in such a case.