A motion is said to be non-periodic when it repeats itself at non-regular intervals of time.
If the motion repeats itself after a regular interval of time then it is called periodic motion.
For example - The motion of a car driving several blocks on a busy downtown street, The motion of my dog on a walk around the block, The motion of fingers as they type on a keyboard, The motion of fingers as they play a song on a keyboard and many more.