That character is a C0 control code (
Wikipedia[
^]).
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Why this character is not visible on website
The HTML standard defines that these control codes must be ignored when rendering output. To show the corresponding symbols the equivalent Unicode symbols can be used (e.g. U+2642 for the male symbol ♂).
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What is the purpose of entering it
How such control codes are handled depends on the application. Some codes like line feed, carriage return and horizontal tab are used to format text. Others like ESC are mainly used during user input. The remaining ones are used by terminals, printers, and serial communication.
With HTML forms you should not allow that any of these characters can be entered (with some exceptions like multi-line edit fields which may except carriage return and horizontal tabs).