I'm not the parent but…

Hit jj instead of <Esc> which many people find too far.

    inoremap jj <ESC>

Exchange ; and : because : is used a lot and you need to press Shift (on an american keyboard) while ; is less used and available without a modifier key:

    nnoremap ; :
    vnoremap ; :

\v means "use verymagic mode for the rest of the pattern", normally, you'd have to use a lot of backslashes to escape parentheses and other "spacial" characters but "verymagic" allows you o type less and obtain more readable patterns. Example:

    /f\(oo\)ba\[zr\]
    /\vf(oo)ba[zr]

With these mappings, search-based navigation is a lot less expensive because it use s "verymagic" by default:

    " Fix vim's terrible default regexp scheme
    nnoremap / /\v
    vnoremap / /\v
    vnoremap ? ?\v
    nnoremap ? ?\v

:cnext, :cprevious and friends are quickfix commands: thay allow you to navigate through the errors displayed in the quickfix window without using the window itself. Even in their shortened form (:cn, :cp, :cfir, :cla) they represent a lot of typing and a good occasion to create much more useful mappings:

    nmap <silent>]c :cnext<CR>
    nmap <silent>[c :cprevious<CR>
    nmap <silent>[C :cfirst<CR>
    nmap <silent>]C :clast<CR>

nmap means "normal mode mapping".

nnoremap means "non-recursive normal mode mapping", see learnvimscriptthehardway.stevelosh.com/chapters/05.html#nonrecursive-mapping

vnoremap means "non-recursive visual and select mode mapping", it should be xnoremap (visual mode only).

<silent> means "don't print the executed command".