What does it mean to have a continuous action space w.r.t. to reinforcement learning?
When you're driving of your car and you turn the wheel, is that a discrete or a continuous action?  It's continuous, because you can control how much you turn the wheel.  How much do you press the gas pedal?  That's a continuous input.  This leads to a continuous action space: e.g., for each positive real number $x$ in some range, "turn the wheel $x$ degrees to the right" is a possible action.