A higher count gives you a much larger resolution. The value the meter detects is converted into a number between 0 and that "count" value.
Let's say you measure a DC voltage, or a resistance on the multimeter.
A 22000 count multimeter can show up to 2.1999v, then it goes from 2.200 to 21.999v, then from 22.00 to 219.99v, then 220.0 to whatever. So especially with low voltages you have the benefit of having 4 digits after the dot, which allows you to spot small changes (for example when slowly loading a supercapacitors from a solar cell, or slowly discharging a battery and so on).
A 6000 count multimeter can only show 0.000 - 5.999 , 6.00 - 59.99v , 60.0 - 600.0v
So it's just a matter of making it easier for you to spot very small changes in the measured value.
It's not accuracy, accuracy could be better on a high quality 6000 count multimeter compared to a 22000 count multimeter but as the 22000 count multimeter gives you an extra digit, it may actually be better for you.