A singles yarn -- also sometimes called a single -- is what you end up with when you spin yarn and it hasn't been plied with another singles yarn. People sometimes call this a "one-ply yarn," but that isn't really accurate because there is no plying going on, there's just a single.
Singles yarns can have difficulty holding together when you knit with them because they lack some of the strength and durability of plied yarns. They also tend to be less consistent because plying can smooth out some of the imperfections that can easily be seen in singles.
Still, spinning singles is how most spinners start out, and you can still use yarn prepared in this way, for example, to knit a homespun flower or another small project that doesn't require a lot of durability or consistency in the fiber.