Aurora Borealis often referred to as the Northern Lights are atomic particles, protons and electrons coming from the solar wind. They travel very fast into space and reaching Earth within a few days. When the solar wind hits the invisible magnetic field surrounding the Earth it´s bounces the solar wind back. When that happens the magnetic force captures much of the protons. This sends them spinning down towards the magnetic poles. Once they collide with oxygen, forming energy that is visible to us as the Northern Lights. The Northern lights are most visible over the Arctic. Here the move like waves and change colours frequently like they are dancing in the atmosphere.
To best experience the Northern Lights here in Iceland the skies need to be clear and darkness is vital. They mostly reveal themselves during cold months where the temperature is around zero degrees and have frequently been associated with cold weather. Regardless of the weather the Northern Lights are dictated by the Sun´s activity and solar storms that erupt releasing those atomic particles. However in reality they shine above any weather system. They just happen to be the most visible to the human eye during darkness and cold temperatures. If you really want to catch them be sure you are in Iceland roughly between September and April.
Since Iceland touches the Arctic Circle the circumstances are ideal to catch those dancing auroras during the winter days. They are in fact visible in the capital of Iceland that is Reykjavik, as well as everywhere where the skies are clear. To experience them in the most efficient way, people often drive to a spot outside of Reykjavik´s light pollution. It only takes about 10-15 minutes to find a perfect spot where there are perfect conditions to fully experience the dancing auroras.
The Aurora is very hard to predict in advance. There are Solar Wind forecasts that can help you see if the Auroras will be likely to behave and dance with you on your desired night. Here is the Icelandic Met Office forecast that might help you. The Northern Lights have shine through poetry and have always been part of the folklore in Iceland. The myth says that if a pregnant woman looked at the Aurora her child would be born blind.