difference between single double and three phase
Here is what wikipedia says about two-phase power. 


  Two-phase electrical power was an early 20th century polyphase
  alternating current electric power distribution system. Two circuits
  were used, with voltage phases differing by 90 degrees. Usually
  circuits used four wires, two for each phase. Less frequently, three
  wires were used, with a common wire with a larger-diameter conductor.
  Some early two-phase generators had two complete rotor and field
  assemblies, with windings physically offset by 90 electrical degrees
  to provide two-phase power. The generators at Niagara Falls installed
  in 1895 were the largest generators in the world at the time and were
  two-phase machines.
  
  The advantage of two-phase electrical power was that it allowed for
  simple, self-starting electric motors. In the early days of electrical
  engineering, it was easier to analyze and design two-phase systems
  where the phases were completely separated. It was not until the
  invention of the method of symmetrical components in 1918 that
  polyphase power systems had a convenient mathematical tool for
  describing unbalanced load cases. The revolving magnetic field
  produced with a two-phase system allowed electric motors to provide
  torque from zero motor speed, which was not possible with a
  single-phase induction motor (without extra starting means). Induction
  motors designed for two-phase operation use the same winding
  configuration as capacitor start single-phase motors.


Single phase and 3 phase are unrelated to 2 phase described above. Basically, 3 phase is what the power stations produce now and ultimately this gets distributed as 3 single phases to our homes: -



There are three line voltages shown in red that are 120º apart in phase orientation. This can be seen as three single phase voltages (blue) and if you did the trigonometry you'd see that the length of red is sqrt(3) times bigger than the length of blue hence, if you have 230V phase voltage, the line voltage would be 398V. Here's how the voltages look in time: -



Going back a few years when the UK had 240V, the line voltage was 415V and sometimes 440V line voltages were referred to ans they yielded a phase voltage of 250V.