^ notation is commonly used in the GNU world for control characters, where
^a is Ctrl-A (ASCII 1 where A is ASCII 65). In other words it is shorthand for "use the character 64 slots before this on".
ESC key is ASCII 27 which is 64 steps before
^[ is shorthand for ESC.
In the GNU Emacs editor several modifier keys were used, CTRL, META and others. For instance CTRL-f moves the cursor a character forward and META-f moves the cursor a word forward.
In order to accomodate the many keyboards without a META key, a convention of "ESC means that the next character is to be considered pressed with the META-key". Therefore in GNU Emacs, pressing ESC-f moves the cursor a word forward.
Note that these days it is very rare that
Ctrl-[ gives an ESC character, but it may be lurking in some other Ctrl-combination. For instance is
^^ still used in telnet sessions to escape to command mode, so it is useful to be able to find it.