Twig is a PHP implementation of Jinja2, a python templating engine. Unfortunately there's no specific syntax highlighting support for .twig files in Vim. But that's no real problem as you can use the htmljinja syntax file provided here: http://www.vim.org/scripts/script.php?script_id=1856
To map it to twig, edit vimrc and add:
au BufRead,BufNewFile *.twig set filetype=htmljinja