What does it mean when multimeter accuracy is marked as: ±0,03%+10Digit?

The 1 digit means that the least significant digit can be off by +/- 1. In this resolution 1 digit would mean +/- 0.001V. 10 digit means that basically of your 79.999V displayed, it could also be 79.989V (not including the 0,03%!)

So basically in your range the 10 digit specification means that +/- 0.03% + 0,01V is your error. For measuring 79.999V it means an absolute maximum error or +/- 79.999*0.03% + 10*0.001V = 0.034V.

Like Hans says +/-1 digit means that the last digit can be 1 off. +/-10 digits means it can be 10 digits off, or 1 digit in the one but last position. It shows how relative 5 digits (actually 4 3/4) of resolution are: while you get 5 digits, only 4 are significant, the last one is not reliable. This may not look too bad, 10 in 80000 is 0.01%, to be added to the 0.03% basic accuracy. However, while the 0.03% is relative to the measured value, the 10 digits are absolute, and they weigh more if your reading is lower. 10 in 80000 was 0.01%, if your reading is 20000 this error will be 0.05%, or larger than the relative error.

If a meter with the indicated specifications is set for the 0-to-80-volt range, small values would be accurate to within 10mv, while larger values could be off by an additional 24mv. On such a meter, the last digit will generally not be meaningful when taking a single reader in isolation, but is provided for use in situations where one is interested in the differences among readings that are taken very close together. For example, if measures two voltages in fairly quick succession, and then repeats those measurements, and the readings are:

Item1    Item2 
49.123V   49.569V  -- Initial measurements
49.125V   49.568V  -- Repeated measurements

one then the difference between the two items' voltages could be safely said to be somewhere between 442 and 445 mV. One wouldn't know where the first voltage was within the range 49.10V and 49.15V, nor where the second was within the range 49.55V and 49.59V, but one would know the difference with a precision much greater precision than one knew either voltage individually.