First and foremost, UI stands for User Interface, making this job title User Interface Designer.
When using a website, most (if not all) people prefer an easy to use interface. They want to be able to go from one page to another, or add an item to their shopping cart, or like a post on Twitter, with ease.
In order to do so, the interface of the site needs to be set up and organized in a way that will easily support the users’ intentions. The people responsible for this interface system is – you guessed it – UI designers!