How does air pressure help predict the weather?

There are 2 types of pressure systems, the high pressure system and the low pressure system.

The low pressure allows for cloud formation, you won't always have clouds associated with a low pressure system, most of the time you will. This system brings storms most of the time. However, you won't always get storms from a low pressure system, you can get them by lake-effect. Lake-Effect storms will only form over large bodies of water, such as the Great Lakes in the US. Depending on the temperature of the lake, it can either strengthen or weaken the storms. Low pressure systems are always associated with stronger storms like Tornadoes and Hurricanes!

The high pressure system doesn't allow for cloud formation, which would bring you great weather.