What does it mean if a chemical or physical property is periodic?
This is the reason that chart in virtually every Chemistry classroom is known as the periodic table.
To be "periodic" means to repeat after a certain interval, like the period of a wave (the time required for the waveform to be repeated) or a periodical ( a publication that is printed after a certain amount of time).
It was long known that the properties of the elements were periodic. If you placed the elements in order (originally meaning by atomic mass, but now by atomic number) you saw that many of the behaviours of the elements would be strikingly similar after you had moved a short way down the list - the reactivity of what we call the alkali metals, the melting and boiling points of the halogens, ionization energy, to name just a few.