The lowest and densest portion of the Earth's atmosphere is called the troposphere. It extends from the surface of the world's seas to between 8 and 18 kilometres (5 to 11 miles) above the Earth's surface depending on latitude (distance from the equator); closer to the surface at the poles (8km) and getting higher the nearer you are to the equator (18km). The mixture of gases contained within the troposphere is what we know as and call air. While the air thins (less gas per volume or cubic area) the higher you get above sea level until reaching the top of the troposphere, its composition, that is the proportions of each gas within it, stays pretty much the same except for one: water vapour.
Air pressure is directly proportional to the molecular mass of the local air. The molecular mass of water vapor is 18.02, the molecular mass of dry air is 28.98. Dry air is all of the components in their respective percentages except for water vapour. Moist air is ALWAYS lighter than dry air; despite this seeming to go against common sense. We typically think of air as having no weight while perceiving water as often being quite heavy. The reason moist air seems heavier to us than dry air is not because of the air, but the moisture held in the air as microscopic droplets of water. Air is a gas and so is water vapour, the more water vapour in the air the lighter it is, but when the limit for the ambient temperature's water vapour carrying capacity is reached, atmospheric water is no longer in the form of water vapour, the excess is in the form of microscopic droplets of liquid water, which are considerably heavier than water vapour.
What this means is that the higher the water vapor content or absolute humidity of air, the lower its mass, and therefore the lower the air pressure. This is where the high and low pressure readings shown in weather forecast maps comes from. Low pressure regions have a high water vapor content and high pressure regions have a low water vapor content. Which is why an approaching high normally indicates clearing skies while a low usually means cloud.
It might be useful to note that the humidity reading usually given in weather forecasts is relative humidity rather than absolute humidity. While absolute humidity measures the actual water vapor content of the air on a mass per volume basis, relative humidity compares actual water vapor content in the air against the maximum possible on a percentage basis. The maximum possible is called the saturation vapor pressure of water, which varies dependent on the current air temperature; the higher the temperature, the higher the possible maximum. For example, if the temperature is 21 degrees Celsius (70 degrees Fahrenheit), then the maximum concentration of water vapor the air can hold is 2.54 percent. Or in other words, in any given volume of air, a maximum of 25,400 parts out of every million (ppm) can be water molecules (H2O). If, in fact, the water vapor content is 19,050 ppm, then the relative humidity is 75%, because the air contains three quarters of the water vapor it could hold.
Since low pressure areas have a high percentage of water vapor, they form over large bodies of water or extensive areas of rainforest in warm to hot regions of the Earth, most commonly the tropics. Evaporation from surface water or transpiration from leaf surfaces supplying the water vapor and the warmer the ambient air temperature the higher the percentage of water vapor it may contain. The higher the percentage of water vapor the lower the average molecular mass of the air and therefore the lower the air pressure.
The structure or anatomy of a forming low pressure area therefore starts with a water vapor providing area of the Earth's surface. Above that is a rising spiral of warm air containing a high absolute humidity, forced upwards by drier air pushing in from the sides. The drier air has a higher air pressure than the moist so pushes it upwards where the air is thinner. The incoming dry air absorbs water vapor in turn, becomes lighter and is forced to rise in turn, so there is a steady flow of rising warm, moist air.
Air gets thinner and colder the higher above the Earth's surface it gets. The warm, moist air cools as it rises, which reduces the saturation vapor pressure. When the saturation vapor pressure and the actual vapor pressure or water vapor content of the air are the same, we have 100 percent relative humidity. From then on as the air continues to cool, micro-droplets of liquid water form in the air, that may be visible as a slight haze. The micro-droplets are held up by the air pressure and continue to rise in the still cooling air that is producing more of them. Micro-droplets impacting with each other join together forming ever larger water drops that become visible as clouds. The continuing up-flow pushes the clouds spiraling outwards in the typical shape of cyclones or hurricanes viewed from space. Although nowhere near all low pressure areas go to that extreme.
The Earth's spinning, the tidal pull of sun and moon and the air-flow from high pressure areas to low pressure areas all lead to low pressure areas moving from where they form. When they move into colder areas or over land, the up-flow of moist, warm air slows or ends. Without that, the low pressure area stabilizes into relatively still, muggy air at surface level until the cooling of the air at cloud level increases the density of water droplets or ice crystals to exceed the ability of air pressure to hold up, and it then rains.