When does a period of the periodic table end?

The periodic table is the diagram used to organize all of the elements discovered in groups depending on a number of different factors. Elements, or atoms with different numbers of protons and electrons, are arranged in rows referred to as "periods." The first period begins with Hydrogen, the second with Lithium, and so on. 

Each element as the period progresses has one more proton and one more electron than the previous element, and these extra protons and electrons give different electronegetivities, weights, and other properties. A row will start over once these properties repeat themselves, thus the element directly under each element shares similar properties as the one above them. This creates columns of similar elements such as the 2nd column which is made up by the Alkaline Earth Metals (all shiny, silvery-white, full S-electron orbital).

Another way to tell a row is about to start over is when you get to an element that has all of its valence electron orbitals filled. This means there is no more room for an electron to bond to in any orbital and it is considered a Noble Gas (Krypton, Neon, Helium, etc.). This marks the end of a row and the next element begins a new orbital as it fills an S orbital spot with an electron to match the one extra proton. 

Once again, a row will start over officially once similar properties start to repeat themselves. All of the first elements in the 1st column have similar qualities, thus they are organized as such, just like the 18th column which all mark the end of a row. Hope this helped!