There are two main types of beehives. They are Moveable Frame Hives and Top Bar Hives. The movable frame hives are a little more complex than the top bar hives. The most common design is still the original Langstroth Hive.
A moveable frame hive like most hives is usually made from wood and has a series of frames hanging in what is called a super. A super is a level of the hive that looks like a box, but has no top or bottom. These supers are placed on tip of each other to form the outside of the hive body. The bees build their combs in the frames. This design suits the professional beekeepers or thos who want to maximise the production of honey in their hive.
The top bar design is basically a long box with wodden bars in a row at the top of the hive. This design is said to be more natural for the bees because in the wild they find a spot and build their comb down from ther much as they do from the top bar. Personally, I would not agree that is would be easier for the bees. If the frame building option was too difficult for them they would not fill the frame, but would simply built to the design that nature intended. Also most beekeepers these days use foundation in the frames. Foundation is a beeswax honeycomb pattern pre-installed in the frame. All the bees have to do is to build on that. Half of the work has been done for them.
This video gives you a good look at what a Top Bar Hive is.