Use "back" to talk about a time period in the past:
Back in the '80s, there was graffiti all over the place in the city.
Back when I was in school, teachers would spank you with a paddlie if you misbehaved.
The time period is usually more than a year ago. It would be strange to use this to talk about something that happened yesterday or last week.
Adding this word makes the time period seem like it was a long time ago.