If the result of a measurement is i.e. $3.2 \pm 0.7$, what is 0.7? At which confidence level we know that the real result is inside of this interval?
The two most common conventions I know are
The 95% interval is often used when one is giving a "normal" range of values - for example, when reporting normal blood sugar levels etc. This is more useful, because it says "if your measurement is outside of this range, you most likely have a problem" - with the usual 5% chance of being wrong.
Without context, there is no way of knowing what the authors intended - although in the example given I would be horrified if this was the standard error (over 20% on either side of the mean)...
My advice - when in doubt, ask. And when it's your turn to report a result, try to avoid possible confusion by saying what you are doing, e.g.
Note - always include units in your quoted result...
As your link indicates, it is the uncertainty in the measurement. The exact meaning of this can depend on context, but most of the time it is safe to assume that this is the standard deviation in the value that you should expect if the measurement were repeated a large number of times.