The word Vorwahl refers to the area code (also known as STD code) of a telephone number.
Area codes in Germany area structured so that it is possible to roughly guess which part of the country someone lives in by their telephone number.
The other part of the number is called the Rufnummer.¬† In the days of dialling phone numbers by hand people left the Vorwahl off the number of they were calling someone within the same Vorwahlbereich, but these days many people program the numbers into their phones with the area code anyway.¬† This saves re-programming when you move, and has also become common practise as mobile phones require the area code all the time.
To call another country, you use the internationale Vorwahl, which basically means putting 00 in front of the country code (eg. 44 for the UK).
The term Vorwahl can also refer to a number dialled in an office environment to obtain an outside line.
To hear a simple explanation and a short discussion in German, listen to the podcast:
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