We sell roof boxes that open from both sides, as well as rear opening boxes and boxes that open from one side.
A left hand side opening box will open from the passenger side.
A right hand side opening box will open from the driver’s side.
Dual-side opening boxes are useful if you are using a wider roof box, particularly if you have a taller car. It's not quite as much of a concern if you are using a narrow box, where it's likely that you'll be mounting it to one side of the car anyway. Fitting a roof box in the middle of the roof may look neater but it's not very practical as you'll have to reach right over to fit and load the box (unless you go for a wider box).
A lot of smaller boxes are rear opening. They are a good option for smaller cars and will often allow you to load the box from three sides. It's not always as easy to use a rear opening box on a larger/longer vehicle.