Awen means "divine or poetic inspiration" in Welsh. The Awen symbol is the creation of the 18th century opium addict and fraud Edward Williams, better known as Iolo Morganwg. He started his illustrious career forging the works of major Welsh poets and is responsible for more misinformation and nonsense about Draoicht and other Celtic practices than perhaps any other person in history.
That being said, several different neodruidic groups have adopted this symbol in various forms. The most notable of these is the Order of Bards, Ovates and Druids, or OBOD. Though its origins are mendacious at best, it is generally accepted today as a symbol of neodruidism. It is for this reason alone I include the symbol in my inventory.
There are three primary beliefs involving the symbolism of the three rays in the symbol. The first and most commonly mentioned is the one proposed by OBOD, that the rays represent light coming from the three aspects of deity. Though beautiful and popular in contemporary culture, this concept would not have been one held by the early Celts, who were hard polytheists. The second explanation states that Awen stands for truth and the rays represent the search for truth, the understanding of truth, and the maintaining of truth. The final explanation contends they represent Earth, Sea and Sky, a very druidic concept.
A lesser-known belief currently gaining popularity focuses on Awen's linguistic origins, and contends that the symbol represents what has come to be known as the Path of Imbas, or the Three Illuminations. The three rays represent Dichetal Do Chennaibh, or the Light of Voice, Teinm Laegda, or Opening of Hazelnuts(wisdom?), and Imbas Forosnai, or Quickened Illumination. I cannot find the original source for this last explanation though I have heard it multiple times, and most of the time the path leads to Searles O'Dubhain, of the Summerlands website.