A 95% error bound merely means that the author thinks, based off several (possibly) sound assumptions, that what we are saying could arise by chance in 5% of cases.
If the graph has datapoints that fit within a 95% bounded line then all you can say is "this data didn't arise by chance in 19 out of 20 cases if the datapoints lie within this bounded path". Typically this 95% probability isn't per point, i.e. when you look at the graph you can't take the fact that each point lies within the bound as repeated 95% probabilities correctly turning out which would combine to a much higher confidence.
In the hopes that this helps,
Richard Feynmann has a lot to say about this, and is well worth listening to.