If this variable is in the environment when Bash starts, the shell enters POSIX mode (see Bash POSIX Mode) before reading the startup files, as if the --posix invocation option had been supplied.
bashをposix modeで実行するための変数。
違いについては bashがsh互換(posix)モードで動く時とか http://itdoc.hitachi.co.jp/manuals/3021/3021313330/JPAS0037.HTMとか