A statement coat is exactly that - a coat that makes a statement. It "makes" every outfit.
You can wear a white t-shirt and jeans and you'll look great. Although most statement pieces are an investment, it doesn't really matter colour, style, patterned or solid as long as it's a coat that has a unique quality to it - usually it has to do with the fine details.
Below are some examples of fabulous statement coats.
The impeccable Anna Wintour I'm sure has several of these types of coats
INA (vintage and high-end consignment)
Decades (vintage & high-end consignment)