This achievement requires that you drive a cumulative total of 100 miles. This can be done with multiple Sims and cars. In order to get this achievement, you will first need a car. There are a few options to obtain one.
Build the car dealership in your town. Then you can purchase a car. The cheapest one is a Prius for $8,900.
Build a property in your town that comes with a car. The mansion is one of them.
Complete enough tasks and eventually you will receive a free, 3-star car. More info on this soon.
Once you obtain a car, you must assign it to a Sim. After doing so, it will be parked outside their place of residence. Select it with the Sim and choose the 3-minute drive (the only option). Depending on the star rating of the car, it could take anywhere between 2 to more than 20 repeated drives to unlock this achievement. There is a bit of randomness involved since the distance the car drives each time varies (there are stoplights around town).