A hex editor is an editor that allows the user to manipulate a file on the bit level by displaying this file as its hexadecimal representation.
A hex editor is a piece of software that allows its user to edit files bit by bit. To achieve this, hex editors display the hexadecimal representation of the file being edited.
Hexadecimal means base 16; after 9 comes A-F, only then comes 10. This is convenient since it means every digit represents exactly 4 bits, which makes it easy to construct and/or recognise specific bit patterns when working with hexadecimal.