There are two main types of gearing used on folding bikes. Internal geared hubs (IGH) and Derailleur gearing. Their are also a few bikes made with both internal hub gears and Derailleur gearing.
The main advantage to internal gearing is the bike will not need a derailleur. Derailleurs stick down below the rear axle and tend to get bent easily.
The main disadvantage to internal gearing is the bikes are usually significantly more expensive and the gear ratios are not very wide.