Air is lifted in and around areas of low pressure. Remember, Air Pressure is the weight of the atmosphere above you. When there is a large area of low pressure, there is less air above so the air at the surface tends to rise. Alternatively, an area of high pressure is like a hill of air in the atmosphere. The air in and around high pressure sinks and spreads outward at the surface.
Another way to think about Low and High pressure is to consider how and why the wind blows. Wind is air in motion. The wind blows from areas of high pressure to areas of low pressure. It's diretion is influenced by the Earth's rotation. Some of this is rising and sinking air (vertical motion) but most of the time when we talk about winds we are talking about horizontal motion along the surface. A forecast of south winds of 12 to 20 mph means the surface winds will be 12 to 20 miles per hour From the south.