The Messinian Desiccation occured during the Miocene, which was the period of time that existed between 23 and 5.3 million years ago. The climate of the Miocene was warmer than both the Oligocene before it and the Pliocene after it. The warmer temperatures allowed for two important ecosystems to emerge: Grasslands and Kelp forests.
The drying of the Sea was called the Mediterranean Salinity Crisis (MSC). The MSC began approximately 6 million years ago (MYA) and lasted until around 5.3 MYA - a time span of well over a half million years! Although scientists are still not completely sure about the cause of the MSC, they do have evidence that offers some explanations.
For example, there is strong evidence that the sea level had dropped about 70 meters (over 200 feet) prior to the Crisis. Scientists believe that this was due to a cooling of the globe. Global cooling would allow water to freeze and form glaciers & icebergs. A large amount of this water would come from the ocean, and with less water, the ocean's level would drop.
This drop in sea level made it difficult for the Atlantic Ocean to flow into the Mediterranean, and the Mediterranean began receiving a much lower amount of water. The Mediterranean tends to evaporate at a very fast pace, because it is located in a dry area. Note that it is located just to the north of the Sahara Desert, which is one of the driest places on Earth. Therefore, the Mediterranean is very vulnerable to drying up if it does not receive enough water.
Meanwhile, the ocean floor beneath where the Atlantic Ocean was connected to the Mediterranean began to rise. Southwestern Europe and northwestern Africa had been moving towards each other. This forced the area between the 2 continents to rise because there was no where else for that area to move. Scientists believe that by 5.59 MYA, the ocean floor had been raised high enough to become an area of land that completely separated the Mediterranean from the Atlantic Ocean. This must have caused the Mediterranean's sea level to drop even more quickly, because at this point the Mediterranean was completely isolated from the Atlantic Ocean.
To see a chart of when this time period occured, please click here.