How to display string that contains HTML in twig template?

Use raw keyword, http://twig.sensiolabs.org/doc/api.html#escaper-extension

{{ word | raw }}

{{ word|striptags('<b>,<a>,<pre>')|raw }}

if you want to allow multiple tags

You can also use:

{{ word|striptags('<b>')|raw }}

so that only <b> tag will be allowed.