Thunderstorms form from three ingredients, moisture, instability in the air and sources of lift. The warm water in large oceans like the Atlantic and Pacific and the gulfs are the major contributors of moisture to thunderstorms. The instable air can come from a few sources in essence each has to provide heating of the air to produce lift, the upward movement of the air. Lift can come from the differential heating that occurs when there is pavement and grass in the cities, from fronts where air masses with different temperatures and moisture content meet, or when air has to go over mountains.
Every thunderstorm starts from a thunderstorm cell which has a life cycle of 30 minutes. The cell starts when cumulus clouds begin grow vertically because of updraft. Once the cumulus cloud reaches about 40 to 60 thousand feet the cell will have coexisting updrafts and downdrafts. At this stage you can get hail, high damaging winds and flash floods. Once the downdraft has overpowered the updraft, the storm cell no longer has a supply of warm moist air and the heavy rain dissipates.
When you have a very short thunderstorm where you hear the thunder, then the storm comes by your location and then the storm stops, this is a single cell storm. When you are in a storm where you hear the thunder, then the storm comes by your location and then off in the distance you hear more thunder, these are multi cell storms. Weather experts call these back building thunderstorms because if you watched the cloud formations carefully you would see the different stages of the storm. Thunderstorms can also create squall lines, with damaging winds and small hail stones, tornadoes, and super cell storms with large hail stones.
Important to note is that sea breezes can greatly effect thunderstorm formation. Florida is at great example of this as it is a peninsula. If there is a 5 to 10 mph west wind coming across the state, this sea breeze will stop thunderstorms from making it to land. However if the same speed wind was coming from the east with no west wind, the thunderstorms would go almost half way across Florida. Also interestingly if there is a calm about the air it is possible a sea breeze will blow in a thunderstorm into Florida, however it will probably only push about 1/3 the way across the state. On smaller peninsulas, such as the northern tip of New Zealand, if a sea breeze is coming in from opposite sides of the peninsula they will collide and create a very intense short lived thunderstorm.