Periodicity refers to the recurring trends that are seen in the element properties. These trends became apparent to Mendeleev when he arranged the elements in order of increasing mass. Based on the properties that were displayed by the known elements, Mendeleev was able to predict where there were 'holes' in his table, or elements yet to be discovered.
The modern periodic table is very similar to Mendeleev's table, but today elements are ordered by increasing atomic number, which reflects the number of protons in an atom. There aren't any 'undiscovered' elements, although new elements can be created that have even higher numbers of protons.