When someone knits with singles, that means they are knitting with yarn that has not been plied. To understand what this means, it's important to know a bit about how spinning works.
In order to make yarn, you take fibre such as wool, flax, or cotton, and you twist it into a rope-like strand. You can do this by hand, with a spindle; or, if you prefer, you can let a spinning wheel do most of the work for you.
Going through this process once creates "singles," sometimes called "single yarn." The yarn is only twisted in one direction (traditionally clockwise). If you dangle the yarn in front of yourself and look at it up close, you can see the twist in it: clockwise-spun yarns have what is called a "Z-twist" because the twists slant upward and to the right, like the middle bar of the letter Z.
Plenty of people knit or crochet with singles, but the twist of the yarn can sometimes lead to unevenness in the finished fabric. Knitters call this bias. The yarn itself also often misbehaves, since the twists can cause it to wrap around itself, tightening and tangling unpleasantly as you progress. Anyone who's knit with singles knows what it's like to have to interrupt their work in order to untwist the yarn.
To avoid creating a biased fabric, you can counterbalance the twist of singles by plying your yarn. What this means is to spin two single yarns together, in the opposite direction that the singles themselves were spun (traditionally counterclockwise). If you do this right, you get what is called a "balanced yarn," where the two sets of twists create a kind of equilibrium and the yarn relaxes.
Most commercial yarns are plied, and thus they have an S-twist (so-called because the twists slant upward and to the left, like the middle arc of the letter S). However, if you don't want to make your own singles, it is possible to buy some; Lamb's Pride by Brown Sheep is probably the most well-known brand of single wool yarns sold in North America.