Parti colours are the colour grouping that includes roans and the "and whites" (black, liver, etc). Roaning is the mix of white hairs in with another colour. The solids are one colour, with no white. The exception is the black or liver and tans, which are produced by solid parents, and also have no white (or very little) so are considered solids.
So for example if a breeder says they breed parti-colours, then they will have roans and/ or black, liver, or orange and whites