Complex spacetime is a mathematical framework that combines the concepts of complex numbers and spacetime in physics. In this framework, the usual real-valued coordinates of spacetime are replaced with complex-valued coordinates. This allows for the inclusion of imaginary components in the description of spacetime, which can have interesting implications in certain areas of physics, such as quantum field theory and string theory.
The notion is entirely mathematical with no physics implied, but should be seen as a tool, for instance, as exemplified by the Wick rotation.