Why do certain areas on Earth have a higher or lower air pressure at sea level?
By way of analogy consider a hot air balloon. The balloon encloses some air. As the air is heated, via massive gas burners, the air in the balloon becomes less dense compared to the air outside the balloon and eventually the less dense air in the balloon rises, lifting the balloon into the air.

Atmospheric air in contact with the Earth does the same thing. Air is differentially heated and cooled due to the effects of the Sun, clouds, cold air injected from polar regions and warm or hot air injected from equatorial regions. This affects the energy of the air and its density. Air density is also affected by moisture; very little over dry hot deserts and more over oceans, lakes, large water reservoirs and forests, due to transpiration from trees.

The temperature differentials result in relatively warmer and cooler spots within the air in contact with the Earth's surface and above it. Air in the relatively warmer spots rises. The height to which it rises will in part be affected by the amount of heat it contains when it starts to rise.

The surface of the Earth immediately below the column of rising air experiences less air pressure than neighboring regions, hence such regions have low air pressure. As the air rises it cools. Eventually, the air falls back down. The area of the Earth's surface below the falling column of air has a higher pressure relative to its neighboring areas, giving rise to high pressure systems.

The seasonal variation of the general locations of high and low pressure systems are due to the differences in the thermal energy of the air, which in turn is determined by the sources of heat and what might be inhibiting heating.



Edit: In Reply to Additional Questions in the Comment Section

If you look at the pictures you provided the links for in your question you'll see that during July there is a low pressure zone over North America in addition to the much deeper low pressure zone over north eastern Asia. Additionally, the north-east Asian low pressure zone extends into eastern Europe and north Africa. The high pressure zones, in the northern hemisphere are effectively “islands” over the Atlantic and Pacific Oceans centered around 30 to 40 degrees latitude. Apart from western Europe and parts of the eastern US coast, northern hemisphere landmasses are under low pressure.

When you look of the picture for January there is a continuous high pressure zone extending from North American to east Asia and into north Africa. There is even a high pressure zone over Greenland. The regions experiencing low pressure are the most of oceans and the equatorial zones – tropical and sub-tropic part of the Earth.

July in the northern hemisphere is the start of the summer and January is well into winter. By July, the landmasses have been accumulating heat from the Sun, since the end of winter, and warming the air above it causing the air to rise and the air pressure to be lower.

Conversely, by January, the landmasses have cooled so they are not heating the air above them. However, air from the northern equatorial region is rising and due to Hadley cells the air falls back down causing the high pressure zones.