Mutt has a builtin line editor which is used as the primary way to input textual data such as email addresses or filenames. The keys used to move around while editing are very similar to those of Emacs.
A or <Home> bol move to the start of the line
^B or <Left> backward-char move back one char
^D or <Delete> delete-char delete the char under the cursor
^E or <End> eol move to the end of the line
^F or <Right> forward-char move forward one char
^K kill-eol delete to the end of the line
^U kill-line delete entire line
^W kill-word kill the word in front of the cursor
<Up> history-up recall previous string from history
<Down> history-down recall next string from history
<BackSpace> backspace kill the char in front of the cursor
^G n/a abort
<Tab> n/a complete filename (only when prompting for a file)
<Return> n/a finish editing
You can remap the editor functions using the bind command. For example, to make the Delete key delete the character in front of the cursor rather than under, you could use
bind editor delete backspace