Network smoothing is an option available in all versions of Battlefield 4. Simply head to Options -> Gameplay to find it. On the PS4 it is set to the half way point but your mileage may vary.
So, what does it do?
When playing online each player’s actions are delayed depending on your ping to the server and any packet loss. Battlefield 4’s game engine compensates for these delays by way of the dreaded “netcode” which estimates where players will be positioned and displays this predicted position. The network smoothing slider allows you to choose how much estimation is used for determining enemy positions (interpolation).
You should adjust this setting to best work with your internet connection. If you have a good connection to servers, you should be able to decrease the setting and see an improvement in how accurately your shots hit moving targets. The aim is to make this as low as possible without affecting gameplay.
When you test any change look for whether infantry and vehicles move smoothly when in motion. If they jump around the screen, it will make aiming at targets difficult, so you’ll want to increase the smoothing factor. If everyone moves smoothly nearly all the time, you’ve found a setting that works with your connection.
Personally, I’ve put mine down to zero and, so far, it’s working fine.