Why do ice cream vendor sprinkle salt on the ice surrounding the ice cream cylinder?

The short reason:

To cool the ice cream and keep it from melting, because salt water and ice is cooler than ice or ice and water.

The more detailed reason:

Salt water has a lower freezing point than regular water.

Ice is never just one temperature, and the molecules of ice always have a distribution of speeds. The fastest molecules are the warmest ones, and the ones closest to melting. If the ice is in equilibrium with some water, the coldest water molecules will be freezing at the same rate as the fastest ice molecules are melting.

Now introduce some salt. This upsets the equilibrium because now fewer water molecules will freeze, since the freezing point of salt water is lower. The ice will melt faster than the water will freeze. As ice melts, it absorbs energy from the environment (called the heat of fusion). So one is creating a system where heat is absorbed from the surroundings of the salt water and ice mixture.

This salt water and ice mixture can be used to cool the ice cream. Ice cream freezes at about 25 degrees F, so one needs more than just ice at 32 degrees F to make ice cream, and to keep it frozen.

An aside:

A salt water and ice mixture will cool down to about 0 degrees F (-18 degrees C). At the time Fahrenheit devised his scale, was the coldest temperature that could be produced in the laboratory (that is why it became zero degrees). Fahrenheit also intended to make 100 degrees the temperature of a normal average healthy human body on his scale (it is really 98.6 degrees F), but he got it wrong (obviously).