The high pressure can mean three things, either the weather in Mexico City is going to be cold, or there's going to be a prolonged rainfall for those four days, and also an option is the combination of the both.
The high air pressure means that the air weighs more than its average, and the air weighs more when the it is colder because the air is getting more concentrated. Also, when it rains, the raindrops make the air much heavier with their weight, so the air pressure is higher.