Single cell thunderstorm
When most people think of a thunderstorm, the single cell thunderstorm is the type they will likely think of first. That's because it is the simplest storm to draw in diagrams and illustrate in photographs. Single-cell storms exists in an environment with little or no wind shear - there can be wind, but it needs to be unidirectional and of the same speed. Thus, these storms clasically form when there is relatively high instability and low shear, typically after a hot, stagnant summer's day, or in the tropics, where wind shear tends to be much lower. They are also known as air-mass storms since they occur within an airmass, rather that at the boundary between two (common with the more severe thunderstorms). In the UK, "pure" versions of these storms are somewhat rare, since there is usually some wind shear - most thunderstorms in the UK exhibit characteristics of several thunderstorm types. 
 
Single cell thunderstorms occur when air close to the surface encounters instability throughout the depth of the troposphere, allowing the air parcel to rise rapidly towards the tropopause, become saturated once it reaches its dewpoint and form a towering cumulonimbus cloud. With nowhere else to go, air returns to the surface in the form of a downdraft, accompanied by heavy precipitation. Because the storm is vertically erect, this effectively "chokes off" the warm, moist updraft which feeds into the storm, and eventually it dies. These storms typically last 30-45 minutes and can produce severe weather elements, such as downbursts, frequent lightning, hail and heavy rain. 
 
Single cell thunderstorm with little to no wind shear to blow the anvil downstream with the upper-level winds.
From http://www.wikiwand.com/en/Thunderstorm
 
The life cycle of a single-cell thunderstorm can be described in 3 stages. 
 
Cumulus Stage 

  • Development of a towering cumulus (cumulus congestus), which is dominated by the updraft. 
  • Nearby cumulus clouds may merge to form a much larger cloud.
 
Mature Stage
 
  • Precipitation, typicallly heavy and sometimes containing small hail, begins to reach the ground. 
  • The downdraft is created when falling precipitation drags some of the surrounding air down with it, and due to the effect of growing cloud droplets making the updraft too "heavy". 
  • Any rain drops which encounter dry air outside or below the cloud evaporate and undergo evaporative cooling, which makes the downdraft more dense, incresing its speed. 
  • Updraft and downdraft are about equal in strength.
  • The downdraft spreads out when it reaches the surface, producing strong and gusty winds.
  • Mature stage represents the peak intensity of the storm.
 
Dissipating Stage
 
  • Eventually the downdraft overwhelms the updraft and the convection collapses because the cloud is vertically oriented. 
  • Precipitation becomes lighter and eventually stops.
  • The cloud begins to evaporate from the bottom up, sometimes leaving behind an "orphan anvil".


 



The three diagrams above illustrate the simple life cycle of the single-cell thunderstorm. They generally last less than an hour becuase of their own built-in self-destruct mechanism (the downdraft), which kills the thunderstorm off. In the diagrams, notice how the isotherms (black dashed lines) curve upwards for the updraft (when latent heat warms the air) and downwards for the downdraft (when evaporative cooling of raindrops cools the air). 
From Markowski and Richardson textbook: Mesoscale Meteorology in Midlatitudes, 2010).