Arcane Focus items are what wizards use to cast spells. That said, it’s a misnomer that this is actually required for spellcasting. While we’ve had a number of magic items with the “arcane focus” tag in recent D&D books, it can be omitted without too much trouble at the DM’s discretion.
While you’re welcome to alter the rules about arcane focus items if you and your players agree for whatever reason that this would be more fun (even if they disagree with how I or Wizards rule now), you should keep in mind that Wizards has published plenty of information on how magic works specific to 5th edition Dungeons & Dragons, and choose whether or not you want to deviate from those materials as a DM at your own risk.
One of the options for this is that an Arcane Focus item can be a spellcasting focus instead, and it makes certain spells (which we cover in the individual class posts like Sorcerer and Warlock) require a non-Focus component. Wizards has not published much on magic items yet in 5E, but when we do we will try to keep the classes and magic items in-line with each other.