The polite form of address in Russian, corresponding to English 'Mr./Ms./Mrs./Miss,' includes two words: first name and patronymic, e.g. Ивђн Петрћвич 'Ivan Petrovich.' This person's full name includes his last name as well, perhaps Ivan Petrovich Kuznetsov. In some situations, the full name will certainly be used, e.g. in correspondence or in the man's passport. But it will rarely be spoken.
The middle name is called the patronymic, because it is derived from the father's first name; thus, the father of Ивђн Петрћвич has the first name Пётр. The patronymic of a woman generally has the suffix -овна rather than -ович, so Ivan's sister would have the patronymic Петрћвна.
The social conventions regarding the use of first names only, first names and patronymics, patronymics only, last names only, etc., are very complicated. A good rule of thumb is to use a person's first name and patronymic until you're advised otherwise. The exception to this is addressing small children, teenagers and perhaps adults in their early twenties, where normally a patronymic is not appropriate in modern Russian.