First you need to see the difference between ''ser'' and ''estar''. while both mean ''to be'' in english, they both are used in completely different contexts in Spanish.
In short, ''ser'' is used to signify more permanent traits of any noun whereas "estar'' is used to denote temporary traits.
e.g. ella está inferma : She is ill
ella es inferma : She is a sick person
See this website for more information:
http://www.studyspanish.com/lessons/serest1.htm
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Now on to fue and era.
Both are past tenses of ser. So both mean ''was''.
However, there can be two types of past tenses. In simple words, One is a DOT past and one is a LINE past. a DOT past is one in which a thing happens at a particular time in the past. a LINE past is when a thing continues to happen for some time.
the DOT past uses the Preterite form of the verb : Fue
the LINE past uses the Imperfect form of the verb : Era
So you will say
Cuando era niño, because you were a child for a long time rather than at a specific time
See this link for more information:
http://spanish.about.com/od/usingparticularverbs/a/era-fue.htm
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Once you have understood that,
the DOT past of estar is Estuve ( Something was at a particular time)
the LINE past of estar is Estaba ( something was for a continuous period of time)
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