What is a cabinet toe space?
A toe space is a recess at the base of a lower cabinet. Generally, 4 1/2 inches high and 3 inches deep, the toe space is there for your comfort.
With your toes in the toe space as you face the cabinet, you can stand very close to the countertop without bending at the hips and straining your back. You can see the toe kick in the illustration below. You're looking at a side view of a base cabinet.

What is cabinet a toe kick or toe board?
Toe kick or toe board is a piece of decorative trim that covers the toe space or subtoe. The toe kick generally matches your cabinet doors and drawer fronts. It covers the front of the toe space, which does not match your cabinet doors and drawer fronts, and covers the seams between cabinets.
In the illustration below, the toe board is white. Again, you're looking at a side view of a base cabinet.