"Time is a wheel with seven spokes, each spoke an Age. As the Wheel turns, the Ages come and go, each leaving memories that fade to legend, then to myth, and are forgotten by the time that Age comes again. The Pattern of an Age is slightly different each time an Age comes, and each time it is subject to greater change." (The Eye of the World, Glossary)
"The Wheel of Time weaves the threads of human lives into the Pattern of an Age, often called simply the Pattern, which forms the substance of reality for that Age." (The Eye of the World, Glossary)
"A person around whom the Wheel of Time weaves all surrounding life-threads, perhaps ALL life-threads, to form a Web of Destiny." (The Eye of the World, Glossary)
Glimmers Q&A - One becomes ta'veren according to the needs of the Wheel. No one is born ta'veren. Rand, Mat and Perrin became ta'veren just before Moiraine appeared.
TSR,Ch15 - Moiraine tells Mat and Rand that two ta'veren in the twisted red doorway at the same time could strain it so much that the connection is broken and they are trapped.
TFoH,Ch30 - Rand's ta'veren effect causes Bael and Jheran to mend the four hundred year old blood feud between Shaarad and Goshien. It causes and constant stream of smaller events as well.
ACoS,Ch35 - Rand's ta'veren effect causes Min and he to arrive at the rebel camp just where Darlin and Darlin are riding. It then causes both of them to talk freely to Rand.
CoT,Ch23 - Verin and Cadsuane get along well despite being on opposite sides of the White Tower rebellion. Cadsuane wonders if this is due to Rand and his ta'veren effect. None of her ter'angreal hair ornaments detects ta'veren.
CoT,Ch29 - Mat begins to accept that his ta'veren nature and the Pattern will do with him what they want.
KoD,Ch3 - Ta'veren can be tracked and located by their effect on the Pattern. Ishamael and Lanfear were good at it, but it is more difficult for the other Forsaken, especially now that the Pattern is in flux.
KoD,Ch21 - Rand's ta'veren effect causes improbable happenings when he visits Tear.