A carriage, especially such as a phäeton, dog-cart, commercial sulky, and such like. It is not applied to a gentleman's close carriage. Contraction of trappings (whatever is “put on,” furniture for horses, decorations, etc.).
“The trap in question was a carriage which the Major had bought for
six pounds sterling.” —
“The traps were packed up as quickly as possible and the party drove away.” —Daily Telegraph.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Trap from Infoplease: