A B-skip is a dynamic running drill that is used as part of a pre-run warm-up routine. It focuses on running technique by focusing on your leg position, posture and foot placement. The extension of the driving leg dynamically stretches the hamstring and then allows you to focus on a strong contact and push off as your foot lands on the ground and pulls through (it feels like a pawing motion).
Start in a standing position with your feet hip-distance apart, look straight ahead, and keep your upper body tall. Raise your left leg to hip height while skipping up on to the ball of your right foot. Kick your left foot up and round to grab the ground so that ball of your foot contacts the ground below your center of mass. Pull the foot through and along the ground (pawing motion!) and push forward dynamically. Continue alternating sides and moving forward.
Just like when running - your arms should follow your leg movements, remember to keep your elbows tucked in. Foot position is also important - keep your foot bent towards your shin (i.e. in a dorsiflexion position).