Wikipedia has:
Uniform interface
The uniform interface constraint is fundamental to the design of any REST service.[14] The uniform i
Ok I think I understand what it means.
From Fieldings dissertation:
The central feature that distinguishes the REST architectural style from other network-based styles is its emphasis on a uniform interface between components (Figure 5-6). By applying the software engineering principle of generality to the component interface, the overall system architecture is simplified and the visibility of interactions is improved.
He's saying that the interface between components must be the same. Ie. between client and server and any intermediaries, all of which are components.