Question

How does the arrangement of elements in periods relate to electron configuration

Answer 1

Electronic Configuration of elements in a period is same because If you see the electronic Configuration of elements in a period you will notice that the valence shell electrons for all elements are present in the same Shell. For example, in first period consisting of Hydrogen and Helium, both the elements' valence electrons are present in the same Shell.
Electronic Configuration of Hydrogen,
1s^1
Electronic Configuration of Helium,
1s^2

Both elements' valance electrons are present in the 1st shell

(This is just a small example to understand the concept because other periods are long but the first period is short that's why I gave the example of the first period)