Hello,
hauptZeile[] is an array of character and the code
if (hauptZeile[hschlecht++] == '\n')
simply checks if the character at index hschlecht is equal to the constant '\n' that is a newline. A character constant is specified between single quotation marks es. 'A', '2', 'b', etc. Special characters are indicated by using the escape sequence: '\n' is a new-line, '\t' is a tab, etc.
It seems that your code is reading characters from the serial port and detects the end of a sentence by checking the new-line character.