I'm no expert, but here's the basics as I understand it. I think of the Earth like a casserole. It's not perfectly even all over the world. There are pockets of granite here and sandstone there, like there are gooey cheesy bits here and meat there.
Same with the air. It's thick here and thin there.
The barometer reads the current air pressure. It doesn't predict the weather. Gravity pulls everything down, even air. The barometer measures how much pressure is being exerted on us.
The sun warms the Earth. Warmed air from the surface rises. When the pressure is high, the air can't rise to the upper troposphere and lower stratosphere where clouds are formed. When we are under high pressure, we are less likely to see rain clouds form. The opposite is true when we have low pressure.
When high and low pressure collide, we are more likely to see storms. Our casserole bubbles over and we have to clean the oven.