The design of the periodic table reflects the observation that many properties of the chemical elements are periodic functions of their atomic number. Along with an atom's valence shell configuration, the periodic properties of an element provide a thumbnail picture of its chemical behavior. The valence plus the atomic radius, ionization energy, electron affinity and electronegativity constitute the 'personality' of an element.
Only rarely to questions appear on the MCAT that ask you directly about periodic properties, but like so many of these early physical science chapters, the material is fundamental to much else which comes later. Of the periodic properties, the electronegativity is especially crucial. Electronegativity difference between bonded atoms determines bond polarity, for example. Understanding bond polarity is necessary for predicting intermolecular forces, solubility relationships or assigning oxidation numbers.