It is an air gap that allows air to escape rather than building up in the pipe and creating an "air hammer" within the pipes (banging noise), and problems with drainage. (think about pouring out of a can that doesnt have the second hole punched in it.

Many locations don't have them on the sink because a vent pipe that goes out the roof that is attached to that particular stack is required. I had never seen an air gap growing up, because in my location its purpose was served by this plumbed in vent pipe.

Keep in mind too that depending on where you are located and what your plumbing set up is, "forgoing" it may not be an option.

A good licensed plumber can tell you what you need both by law and for safety.

you need to be more specific.

Is this vent under the countertop or above it with a connection directly to the dishwasher ?

The purpose of an air gap is not really to allow air to escape but rather to keep dirty water from back flowing into the DW

An autovent allows air into the system to allow for proper drainage and an air gap is not dependant on one or vice versa. The autovent takes the place of a vent stack to the roof.

Autovent also called air admittance valve, or Studor Vent (brand name).
Casey

OP was asking about air gap, calling it air vent.
This confuses some of the answerers.

All the above info is correct.
What I am about to say here is not a contradiction.

"Gap" is before the P trap, on the room air side.
"Vent" is after the P trap, on the sewer air side.

As for air gaps, they may be overkill. Many think they are.
Every dishwasher has a drain hose that either goes up to the air gap, or else
it goes up "high" to make a high loop under the counter before going back down to
its connection to the plumbing.

This hose connection is always somewhere before the P trap, not after the P trap.

High loops are fine.
Air gaps are more better.
Why? For a few reasons that require a large number of words and are best given by an expert on public health and the water system.
Even Master Plumbers argue about it a lot.

Executive summary: it's nothing to worry about.