From Civ World
Weather is a feature of battles that affects the strength of certain units fighting in the battle. There are four kinds of weather during battles:
The current weather for a battle is displayed as an animated background behind the unit cards. One type of weather is active at a time, and each battle will change between types of weather at random intervals.
Each military unit has an attribute based on the ideal weather condition for that type of unit. All units fighting in a battle that favor the current weather will have their attack or defense strength doubled for as long as the weather lasts. When the weather changes, these units will return to normal and a different set of units will have their strength doubled.
Each unit card shows its favored weather as the card background, behind the image of the unit.