The screen in your sink is part of the aerator system attached to the end of your faucet. The aerator keeps the water from spraying out of your faucet at a high force. It also adds oxygen into the water. This keeps the water from clouding up when it comes out. The screen also acts as a filter and removes some particulates from the water. Because of this, eventually the aerator screen will start to clog, restricting water flow. When this happens, remove the screen, clean it or replace it.
Search for the aerator at the end of the faucet. They look different depending on the type of faucet you have. In most cases, they thread to the inside of the faucet and protrude from the end.
Grip the aerator housing with a pair of pliers and turn the aerator housing counterclockwise to unthread it from the faucet.
Pull the internal parts out of the aerator housing. Make a mental note of how each part comes out so you can reinstall the aerator correctly. The metal screen is the last piece to come out of the aerator housing.