What uncertainty does an error bar signify in astronomy? When an astronomer talks about her/his topic and shows an X/Y-plot with error bars. What should one assume that those error bars represent?
1 standard deviation? Or 2? Or some specific significance level like 95% or 99%?
Is there a generally understood convention for this, or does it vary depending on topic? I've noticed that it is very rarely explicitly stated what the meaning is of the range which the error bars cover.

And how are the cases treated, where exact observations reveal a variation in the actual population? Not "errors", but natural true certain variation. Are there other bars to illustrate that range of true values, as opposed to the variation due to observational uncertainty?
In a published scientific paper, the significance of any error bars should be explained. If this has not been clearly stated then peer review is not doing it's job. However, in some fields there may be unstated conventions which slip through without explanation. 

In my own field (star formation) plots which shows averages over a large data set would show means with error bars representing one standard deviation, while plots which show single measured values might have error bars representing calculated uncertainties on the measurement, for example due to detection limits or instrumental uncertainties.