An arcane focus can be as simple as a magically charged object.It usually grants you one free spell of a given level per day and/or certain advantages for the use of spells cast with it.
Many powerful entities collect magical objects, like scrolls, rings, wands, staffs, figurines or crystals to acquire their powers. A Wizard who possesses an Arcane focus is granted one free spell of a given level per day and/or certain bonuses to the spell’s power if they possess that prerequisite level.
Alternatively, an arcane focus may grant an extra metamagic option on your spells at all times so long as you have the requisite pre-requisite caster level or higher.