-> is a dereference operator; it has nothing to do directly with MySQLi. That is used with objects. The object section of the API can help describe these: http://php.ca/manual/en/language.oop5.php
OOP is a completely different paradigm from procedural code. Logically it is simply a structure of variables and methods that operate individually on an instance of a class. So two objects can call the same methods, yet the operations within them are likely using different data. So think of it as a mini sandbox that you can play in.