Threephase power, or
polyphase power is indeed distributed from the power company with three
hot wires (with
voltages 120 degrees out of
phase) and a smaller,
neutral wire, which is the
ground.
Assuming a "balanced" load, the instantaneous power delivered to the load is constant in time, as opposed to pulsating with a singlephase power source. This is one of the attractions of threephase power.
The typical threephase power connections are the wye and the delta connections. These are the two "canonical" balanced connections that you often see in textbooks.
The
wye connection is shown below.
A,
B and
C represent the three hot lines and
n the neutral. The
phase voltage between each of
A,
B and
C and the neutral is
V_{p}, each 120 degrees out of phase from the others. The
line voltage V_{l}, the voltage between two hot wires, is 3^(.5)*
V_{p}.
_____
 
A  Z 
_____ 

_____ 
  
B  Z 
_____ 

_____ 
  
C  Z 
_____ 


n 
It turns out that if each of the loads Z are identical, no current flows on the neutral wire at all. This is called a balanced load. Therefore, the neutral wire may be totally omitted. Balanced loads are not usually the case in the real world of course, and a small amount of current flows along the neutral wire. This is why it is present (but smaller).
The delta connection is shown below. A, B and C represent the three hot lines. Note that the neutral is not included here, as it is unneccesarry.
A 
 
____ 
  
 Z  
_____ 
 ____
  
B   Z 
 _____
____ 
  
 Z  
_____ 
 
 
C 
There exist
wyedelta and
deltawye transformations to represent one type of load in terms of the other. The voltage sources, which were not shown here, may themselves be connected to the load in either a wye or a delta configuration.
Most industrial threephase voltage supplies are either 480 volts or 277 volts RMS, compared to 120 volts for residential usage. There are many threephase applications where the ground wire is needed, and some, such as threephsae motors, where it is not. You will find a mixture of these in the industry.