Mixing RAM means that all the RAM didn't come as a set. So in your case you originally bought a dual channel kit and now wish to add another dual channel kit.
Some people mistakenly assume that just because they purchased the exact same kit with the same part number for the second set, then they match. In some cases this is incorrect. Sometimes the manufacturer can't obtain the same RAM chips that they started a kit with, so they change them to something else. Everything about the DIMMs with the different RAM will look the same, like PCB, heatspreader, etc. However because the RAM is different it may have slightly different timings (not usually primary timings, but sometimes secondary timing, and tertiary timings) and may even have different voltage requirement.
The above situation is the best case scenario, your chances of both kits working together is pretty good. However mixing brands, and / or models is a much sketchier proposition. What is worse is in many cases it may appear to work fine most of the time. However you may experience very random problems that could be very infrequent in nature and be hard to narrow down to a mixed RAM issue.
I've mixed RAM and had it work. I've also mixed RAM and the system simply wouldn't POST. However for the least amount of headache, it's almost always better to replace the entire kit with a new larger kit rather than add to what you have.
Another thing to consider is the more DIMMs you have the greater demand that is placed on IMC. Depending the the CPU you have this could manifest different kinds of problems. If you are using high frequency RAM, and one kit worked fine at its non-JEDEC speeds, you may find that with two kits you are unable to use the faster profiles. If you overclock your CPU, you may find that your once stable settings are no longer stable with the addition of more DIMMs.