concept of segmentation in cellular communication
Let's consider an old-fasioned analog cell system to easily see where the benefit comes from.  You get the same benefits in current digital systems, it's just a little bit obfuscated due to how the protocols work.  

If a cell phone wants to make a call, it gets assigned a unique frequency channel.  This frequency channel has to be 'clear' between the cell phone and the base station - nothing else in range can use the same frequency.  Let's say you have 100 channels and you put one base station in the middle of a city.  With this system, you can handle up to 100 simultaneous calls for the entire city.  

Now, let's add cells.  Take that same city and break it into a 10x10 grid of 100 cells.  Put one base station in each cell.  Divide the 100 channels you are using into 4 groups of 25 and assign them to the cells in blocks so that no adjacent cells use the same block of channels.  Something like this:

ABABABAB
CDCDCDCD
ABABABAB
CDCDCDCD


Notice that there are no adjacent letters in rows, columns, or diagonals.  Make sure that the transmit powers of the base stations are low enough to not interfere with cells that DO use the same frequencies.  Under this condition, the same channel can be used in multiple cells because anything else using the same channel will be far enough away to not interfere.  In this case, you can now service 25 calls per cell, of which there are 100 cells = 2,500 simultaneous calls.  The flip side is you can only service 25 simultaneous calls in each cell.  

Where you gain is in the ability to reuse spectrum repeatedly due to the relatively small cell size.  You also gain in the fact that the required transmit powers are lower due to the proximity to base stations.  The main downside is that you can only support a relatively small number of calls per cell.  

Modern digital systems use techniques like code division multiple access (CDMA) to allow multiple calls to share the same frequency channel.  Modern cells can also be subdivided further with directional antennas.  This further improves capacity by allowing 1 base station to cover more than 1 discrete region.  Generally 120 degree sector antennas are used to divide a cell into 3 parts, but it is possible to subdivide further or to provide spot coverage to high density areas.  Frequency reuse gets a bit more complicated due to the antenna configurations as well.  Generally the more beams you have (some antennas such as phased arrays can provide much more than 1 beam), the more bandwidth you can provide, assuming you have a good system for reusing frequencies.  

Edit: corrected numbers; originally thought you have to have 9 blocks to ensure no adjacent channel blocks, but 4 also works for a square grid assuming 1 cell separation is sufficient to reuse channels.