Newton’s first law states that a body continues to be in its state of rest or uniform motion unless a net external force is applied on it.

But, when we consider a vehicle accelerating, it increases its speed internally right? Or if a man running with uniform speed increases his speed, the force is internal right?

See that the force a car generating is to rotate its tires, the tires rotate on ground and the tires are actually applying a force on ground and by newtons 3^rd law the ground also provides an eqal and opposite reaction which in turn push the vehicle forward, same as the case of man when we push our feet backward we get a reaction forward which will move us forward so you are getting an external force in these cases. If you Imagine a man walking on a fricionless floor will have no rection so he will not move forward if he accelerated to any amount so here you should assume ideal conditions to get a straight forward meaning of the statement. Becouse the law is used in wide rage of applications you should attempt some questions to get “how to apply the law”.