The occurrence of the elements with similar properties after certain regular intervals when they are arranged in increasing order of atomic number is called periodicity.
The periodic repetition of the properties is due to the recurrence of similar valence shell configuration after regular intervals. The element in a group has the same valence electrons thus similar properties.
In a period, the tendency to gain electrons increases from left to right. This tendency increases because the hold of the nucleus on the outermost electrons becomes weak thus it becomes easy to eject the electrons.