A traffic case will not go away just because you ignore it. Failure to appear can cause increased financial costs, license consequences or even custodial arrest.
The progression that occurs when you do not show up on a case made on a uniform traffic citation depends on whether or not it is a "serious traffic offense." A serious traffic offense is one that you typically would have been arrested on and required to post bond. Examples are DUI, reckless driving, vehicular homicide, and a handful of others. Everything else is a non-serious offense, even those charges that the court may require personal appearance for.
If you fail to appear for the first scheduled court date on a non-serious traffic offense, the court will send out a "courtesy notice" assigning you a new court date at least 30 days out from the first appearance date. If you fail to appear for the second court date, the court can then file a Failure to Appear (FTA) notice and send that information to Georgia Department of Driver Services. A copy will also be sent to the driver. At that point, additional fees are added to the ticket at the local level and lifting of the FTA will require a fee at the state level, which will be paid to the Georgia Department of Driver Services. The FTA will suspend the driver's privilege to drive in Georgia or the Georgia driver's license or permit. Generally, most other states will honor that suspension and, if so, would suspend the driver's license.
The traffic court is not required to send a courtesy notice on a non-appearance. The court will issue a bench warrant, which allows for the arrest of the person. If the driver is out-of-state, this can result in the driver being held several days in the other state while the law enforcement agency determines whether the offender will be extradited from the other state and those issues are worked out. Once the person is back in the local jail or detention center, they may be held until the next court date.