Weather models divide the atmosphere into cells where each cell has it's own forecast. There are several ways to do it but if you imagine the cells as cubes, the north-south and east-west dimensions of the cube is 300m long. 300m is very high resolution for weather models with most running at a few kilometers to a few dozen kilometers.

It means that the underlying weather data is computed and validated at a 300x300 meters resolution. Hope this helps :)

How are you doing validation?

Also note that it should be "300 meter resolution". You don't use a plural when using it as an adjective. I only point this out to help people because this is a common grammar mistake for non-native speakers.