What input lag actually means
Input lag is the time between an action on your controller and the moment it shows up on the screen. Every TV processes the incoming picture before displaying it, running it through noise reduction, motion smoothing, and upscaling. That processing takes time, usually measured in milliseconds, but in a fast game those milliseconds are the difference between landing a shot and missing it.
It's separate from refresh rate, which is about how often the picture updates. A TV can have a fast refresh rate and still feel sluggish if its processing pipeline is slow. That's why two TVs with identical refresh rate numbers can feel completely different with a controller in hand.
