Weather conditions affect wildfires in three key ways that can lead to easier suppression or an out-of-control blaze. The three major factors for the development or suppression of a wildfire are wind, humidity, and air temperature.
Wind is the most obvious driver of a wildfire. As the wind picks up it flattens out the flames, bringing them closer to ground level vegetation. When the flames are closer to the ground, vegetation heats up and dries faster. This can lead to a fire quickly intensifying and spread rapidly. When wildfires are intense they can also create their own weather patterns making conditions around the fire extremely dangerous for firefighters.
The relative humidity is most simply how much water the air can hold. Humidity is extremely important for taming a fire. The drier the air is the faster vegetation dries out, which intensifies a blaze. Consistent rain, even if it is only a small amount, is key for fire suppression. Humidity saps large amounts of energy from wildfires so even if there is no intense downpour consistent high humidity can help fire crews.
Fire needs three ingredients to ignite: fuel, oxygen, and heat. In a forest, both fuel and oxygen are readily available. The main job of fire crews is to eliminate one of those three ingredients. Hotshots spend much of their time digging fire lines which eliminates fuels on the ground so the fires cannot advance. When air temperatures are cooler fires tend to grow at slower rates. This is due to the fuel simply being cooler, which means it will take more energy (heat) to make those materials combust.