The flag is a collage of the flags of the six Celtic nations (clockwise from upper left): Brittany, Isle of Man, Scotland, Wales, Cornwall, and Ireland. I don't know the exact name of the emblem at the centre, but there is, at the British Museum, a very ancient bronze enameled shield by La Tène culture, from early 1st century BC, which has three circles in vertical disposition, the middle one bigger than the others, which has similar wavy patterns forming intricate designs, though not the one seen at the flag. So, the symbol has to be very ancient too.
Linguistically, the Celtic culture (barely) survived only in the peripheral areas of the British Isles and in the French Brittany. These are the areas to this day more Celtic in nature. But throughout the northwestern Iberia (Spanish Galicia and Asturias and the Portuguese Trás os Montes), Celtic roots survived intensely in traditions and folklore. This area is a sort of second
league in the ranking of "Celticness", despite having a Latin language (four of them, actually: Galician, Portuguese, Asturo-Leonese and Castillan). The flag above would be a flag of the first league, those areas with not only Celtic culture, but also Celtic language.
The symbol in the center is a Triskell (in Breton Gaelic). It's a very old solar symbol. The meaning is the cycles of the universe : the years, the seasons, Life and Death etc.... It's a very positive and powerful symbol in our traditions.
The emblem at the centre of the Collage Celtic Flag is called the triskele. The insigne of the Isle of Man, three human legs radiating from a central point, is another form of the same motif. The spiral triskele shown on the flag is a very ancient Celtic design, and one of the most frequently found symbols at ancient sites inhabited by Celtic people. I have seen the abstract spiral triskele, such as the design at the centre of the flag, described as a sun symbol and a symbol of fertility and/or pregnancy. Though it predates Christianity in the Celtic countries, some Christians prefer to think of it as symbolising the Trinity. Like the triquetra or 'Trinity knot', a related ancient Celtic symbol, the triskele is sometimes considered to represent the triplicities of mind, body, and soul, the three domains of Earth -- earth, sea, and sky -- or the pagan Triple Goddess in her triad manifestations of maiden, mother, and crone.