Mopeds are typically divided into two types: Step-through and Top-tank. It's tough to define one without the other. A step-through is basically a moped where the frame proceeds downward from the triple tree and handlebars, and either levels off or begins to curve or angle back upwards towards the seat. Basically, this would allow someone approaching the moped from the side to 'step through' it by passing between the handlebars and the seat, stepping over the lower, leveled-off portion of the frame. This is in contrast to a top-tank, where a frame component directly connects the handlebars to the seat area, so that a person approaching the moped from the side would run into a frame component if they tried to step through it, so they'd have to climb all the way over instead.
Examples of a step-through moped include: