The first time I saw a single-leg squat I thought, “No problem.” Well, guess what happened when I tried to do one? I landed on my bottom and my ego was not the only thing left bruised.
One-legged movements are great for balance, not only for the standing leg, but also for building balance between legs. When doing one-legged exercises, it is easy to detect imbalances and asymmetries between your legs. Correcting these asymmetries is especially important for injury prevention. I know this firsthand, from having a severe car accident that damaged my right leg. I have had to work really hard to balance things out.
Single-leg squats are also great for proprioception, so your muscles can react more quickly from a stumble. Ahem, trail runners and clumsy people: this will help with those out-of-nowhere tumbles. Additionally, this little gem of an exercise works the stabilizing muscles in the ankles, hips, and low back.
This flow would be appropriate to do before a lifting session with squats, performing a workout with single-leg squats, or running.