What does the notation "± (0.7%+3)" mean? Specifically, what does "+3" mean?
The "+3" in that context, is the number of least-significant digits (LSD) on that range, which can be in error. This notation is one of a few "industry standard" ways of specifying measurement accuracy.
The accuracy specification you quoted is from the 2V range of whichever meter that is in the question. Therefore using that as an example, the accuracy on a reading on the 2V range is between:
(reading +0.7% +3 LSD) and (reading -0.7% -3 LSD)
I found the Etekcity MSR-A600 meter has the same specification you quoted, so I'll use that one to illustrate LSD a little more. That is a 3.5 digit meter i.e. maximum count = 1999. The maximum count value is important for this next calculation.
For a 3.5 digit meter, on the 2V range (actual maximum value shown is 1.999V) the LSD value is 1mV (0.001V). The value of the LSD will vary on other ranges.
So the accuracy calculation on that 3.5 digit meter's 2V range, is:
reading ±0.7% ±3mV
(where the 3mV is the 3 LSD, on that range, on a 3,5 digit meter)
The percentage of reading is the gain accuracy; the number of LSD is the offset accuracy. They relate to different parts of the measurement process and so have different units.
Some more explanations, for future reference and showing more "worked examples" for different meters:
