Can you explain the function of neutral gear of an auto car?

When you slow down in gear and come to a stop, the engine at idle is still turning the torque converter but not at a sufficient speed to create any positive drive, it will idle along at a slow speed but with the brakes applied the transmission will not drive, think of the torque converter as a fluid clutch the faster the engine speed the more drive no engine speed little or no drive. Neutral shifts a valve with in the transmission valve body that re directs the oil pressure away from the servos and dumps it back into the sump, so you have no drive, there is no advantage to selecting N at light the wear in components in selecting is extremely marginal at best and for my money its less safe selecting N as in an emergency for what ever reason it would be best to leave in gear and have instant drive then be fumbling about looking for gears in a panic situation.

It won't save fuel but it could save a little wear on the brakes from not holding them applied in one spot when they're hot. That COULD potentially reduce the chance of a rotor warping, (over its lifetime). That's a very little deal. I just let my vehicles creep ahead a few inches at a time to prevent that uneven heating.

Every time you shift into drive or reverse there are rotating drums that suddenly come to a stop when the clutch plates engage. They will slip until enough pressure builds up to make them lock up and that slippage is where most of the wear takes place. That's the clunk you feel when you shift into gear. Once they're locked up, it doesn't matter if you're standing still or on the highway, no clutch plate wear is taking place. Think of it as starting out from a stop with a manual transmission. You can't just slide your foot off the clutch pedal and let it grab instantly. You have to release the pedal slowly and allow the plate to slip less and less as the car starts moving. The clutch packs in an automatic are doing something similar but to a lesser degree.

The only advantage to shifting to neutral is when the engine is running hotter than normal, it can reduce the drag or load on it and that can reduce the temperature a little. That is for extreme conditions though. When waiting for a really long red light, leave it in drive for the comfort of your passengers if nothing else. That's how it was designed to operated.