Gear score is a numerical value based on the statistics of a player's gear. It is (supposedly) the maximum potential of a player's performance.
Gear Score in Black Desert Online is based on your both your Attack Power as the Awakened Attack Power and your Defense Power. You can find the values beneath your gear when pressing I.
A higher Gear Score means you are able to grind in more difficult areas. For example you can comply with the minimum required AP but at a higher Gear Score you are able to easier grind in that area. However, it is up to the player to perform that well.
After calculating the Black Desert Online Gear Score you can see the bonuses you receive for the AP and DP bracket you currently in to. Next to that you can also scroll to all the available brackets to see the bonus you can gain in the next available bracket.