Understanding the relationship between resolution and accuracy will help you determine how small a voltage, current, or resistance—or how small a change in those values—you can actually measure with your digital multimeter.
When you buy a digital multimeter, the first thing you normally look at is how many “digits” or how many “counts” the multimeter displays. The more digits or counts that a multimeter has, the higher the resolution with which you'll be able to make measurements. The number of digits is directly related to the number of distinct values that the DMM's analog-to-digital converter can output.
A 3-1/2 digit DMM, for example, can display up to 2000 distinct values, or “counts,” ranging from 0 to 1999. The most significant digit in this case is either 1 or 0. That's why it's called a “half digit.” A 4-1/2 digit DMM can display up to 20000 counts. The latest generation of DMMs has done away altogether with the notion of digits. Instead, they specify the display resolution only in counts.
The greater the number of counts, the higher the resolution. What that means is that the more digits your DMM has, the smaller the change in voltage you can measure. For example, a 6000-count multimeter like the Fluke 83V can measure from 0 V to 5.999 V on the 6.000 V scale and has a resolution of 1 mV.
Resolution isn't the whole story, though. For one thing, digital measurements always have an uncertainty of ±1 count: when your 6000-count DMM displays 3.000 V, the actual value could be either 3.001 V or 2.999 V.
In addition to the digital uncertainty, you also have to take into account the analog accuracy specification when determining how small a change in voltage that you can actually measure. The Fluke 83V has a DC voltage accuracy specification of ±0.1% of reading. If you're trying to make a 3.000 V reading with this DMM, you have to add another 3 mV of uncertainty. When you add the analog uncertainty to the digital uncertainty, you can see that your 3.000 V reading could now actually be as high as 3.004 V or as low as 2.996 V.
Many other factors affect the accuracy of a measurement. The Fluke 83V data sheet, for example, notes that the accuracy specifications are only good when operating the DMM at an operating temperature of “18 °C to 28 °C, with relative humidity up to 90%, for a period of one year after calibration.” If you're operating the DMM in warmer or colder temperatures, or in very humid conditions, you can't expect the highest accuracy.
It's also important to note that the accuracy specifications are only guaranteed if your meter has been calibrated regularly. If accuracy is important in your application, be sure to have your DMM calibrated every year or whatever calibration period the manufacturer specifies.