Google trust rank is an algorithm believed to determine search engine positions. It assesses your website to see how trustworthy it is to improve the effectiveness and relevance of its search results.
There are many things that could affect your trust rank including:
Domain age
Number of links you have
Page Rank of the website that links to you
Trust rank of the site that relate to you
Controversial topics such as gambling or pornography
Spam on your site or sites that link to you
Length of a domain registration
Regular updating
Unique IP address
Displaying a privacy policy
viewing contact details including an address
Security certificates

The main factors that will probably influence your trust rank are the age of your domain and the quality of the website that is linking to you.
The main point to remember with both trust rank and Page Rank is to ensure everything you do is for the right reasons and that it is ethical.
If you make sure you are not doing anything that you believe could be interpreted as bad practice, the chances are your website will be beautiful.
Google’s trust rank is not recognized by Google as an existing algorithm; it is just a phrase to describe an effect often seen in practice.