"A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force."

Newton with this law actually is trying to say that there is a natural tendency in every object to keep their initial state if there is no net force resulting from unbalanced forces acting on it (if all of the external forces acting on the object cancel each other out). That means, if the object is at rest to continue being at rest or if it is moving with constant velocity, to continue moving with that constant velocity. If an additional external force is applied, the velocity will change. This is also used as a definition of inertia.


Figure 5:
Source: http://teachertech.rice.edu/Participants/louviere/Newton/law1.html


Figure 6:
Source: http://www.physicsclassroom.com/mmedia/newtlaws/il.cfm

Example: If we have a ball at rest on frictionless surface, the ball will continue to remain at rest until is being pushed (applied force). Once in motion, it will continue moving with constant velocity in one direction as long as another force causes it to stop or change direction.