The Wizard is the utmost Arcane scholar. Many countless hours spent studying ancient tomes, practicing complex cantations and daily memorization of spell verbals and reagent requirements have lead them to master the leylines of magic.
Spells are an open ended toolbox that can help ones adventures in countless ways; from basic damage dealers, to arcane armours, to complex illusions, or simply levitating a 5lb object. The known Spells are crafted by great archmages throughout history, molding the various properties of magic to a specific and honed purpose, only just barely safe enough to be willfully torn away from the extraplanar realms native to these energies by the common Wizard and utilized. There are eight schools of magic, and varying degrees of complexity for spells available to wizards of different experience levels; the schools of magic are Abjuration, Conjuration, Divination, Enchantment, Invocation, Illusion, Necromancy and Transmutation.
The Wizard must choose which spells they are going to memorize and use daily, limited by the capacity of ones intelligence, for as mentioned above spells require memorization of complex verbal and reagent requirements... failing to properly speak the correct arcane syllable or misplacing Hogwart for Eye of Toad could lead to disastrous results in the attempt to cast a spell.
So a good Wizard must truly learn to understand the potential applications of the spells they choose.
Of course the most important ability for the Wizard is Intelligence. It determines how many spells you can cast per day, as well as influencing many of their most useful skillsets, such as deep Knowledge on many areas, including history, languages, geography etc.... The following most useful statistics would be Constitution and Dexterity, simply to keep the Wizard alive, for they are unable to wear traditional armour as it interferes with arcane spell casting.