Ballast is resistance in series with the ignition coil primary. Sometimes it's a separate resistor, sometimes a length of resistive wire, and sometimes the coil is made so it has enough resistance by itself (called an "internally ballasted" coil). Without some resistance somewhere, you get too much current in the coil and it will actually get quite hot, even burn out.
The separate resistor, if you have one, is usually a ceramic brick about 3" long. If the coil is "internally ballasted" it will measure something like 3 to 4 ohms and there will be no external ballast resistor.
Electronic ignitions are specifically designed to work with or without ballast. For example, the Crane XR700, which I use, requires either a ballasted coil or external resistor. The Crane XR3000, however, specifically must not have ballast resistance. So, if you install an electronic ignition, you need to be sure you have the right kind of coil.