A Sol is the power source of the Twilight Realm. They are the physical equivalent to the sun from the world of light. Before Zant's invasion of Hyrule, he sealed the Sols away with the help of Ganondorf, and covered the realm with darkness, and proceeding to merge the Twilight Realm with Hyrule. Link restored the power of the Sols, bringing light back to the Twilight Realm. The power of the Sols was transferred into the Master Sword, allowing Link to cut through the darkness with the new Light Sword. They are also the only objects from the twilight realm that aren't twilit themselves.
There are two Sols that Link must find to create the Light Sword. Each is guarded by a Zant's Hand, which can move through walls though apparently cannot travel outside. Sols can be placed in special pedestals that activate something, such as a floating platform. The Sols hold the power to transform Shadow Beasts back into Twili.
It is unknown whether they provide heat as well as light.