The elements in a group tend to have similar physical and chemical properties because of their similar outer shell electron structure.
A Period is a horizontal row of elements with a variety of properties, changing from very metallic elements on the left to non–metallic elements on the right. A period starts when the next electron goes into the next available main energy level or shell (Group 1 alkali Metals). The period ends when the main energy level is full ie reached the Group 0 Noble Gases.
All the elements on the same period use the same number of principal electron shells, and this equals the period number (e.g. sodium's electron arrangement 2,8,1, the first element in Period 3).
The first element in a period is when the next electron goes into the next available electron shell or energy level (i.e. 1 electron in the outer shell, after H it is the Group 1 Alkali Metals like sodium 2.8.1).
The last element in a period is when the outer shell is full resulting in a very unreactive element, the Group 0 Noble Gases e.g. argon 2.8.8. The next electron for the next element goes into the next highest level (shell) available, and so starts the next period with a group 1 element again, periodicity – a very similar element every so often – but governed by the electron rules.