Uniform rectilinear motion (URM) is a straight-line movement during which the speed is constant.
In a MRU, the distance covered per second remains the same. This is why the motion is said to be uniform, since it has the same variation of position for any given time interval.
The term rectilinear refers to straight-line motion. For complex motion involving movement along more than one axis (e.g. projectile motion), it is simpler to analyze the motion by breaking it down into a number of simple movements. This decomposition can then be used to study the various parameters of straight-line motion.
To fully understand MRU, it's best to use a graphical relationship to better understand the variations that occur during the movement of an object. These relationships are explained on the following concept sheets:
A car with its cruise control activated covers a constant distance every second.
When a moving object accelerates (or decelerates), it travels in a uniformly accelerated rectilinear motion (UARM).