Era = Imperfect of "ser"
Fue = Preterite of "ser"
The imperfect is used to describe events without definite beginnings or ends, such as describing the circumstances in which an event took place and continuous actions in the past.
The preterite, on the other hand, conveys actions that were started and finished in the past with definite beginnings and ends.
For "ser", here are some examples.
Ella era una niña cuando yo vivía en Valladolid.
She was a child when I lived in Valladolid.
The state of being a child is continuous in the past, and doesn't really have defined beginnings or ends. Similarly, you say "vivía" as opposed to "viví", because you lived in Valladolid for an extended period of time, without a specific timeframe. Here's an example with "ser" in the preterite.
Él fue el padrino de bodas por su amigo.
He was the best man for his friend.
Here, the "él" in question was a best man, but his being the best man was a one-time thing, a condition that doesn't continue further in the past.
I hope that helped!