Final answer:
An incompressible fluid in this scenario ensures constant density throughout the fluid.
Step-by-step explanation:
When a fluid is described as incompressible, it means that the density of the fluid does not change. This means that every cubic meter of the fluid has the same number of particles and there is no room for more particles to be added. The significance of the fluid being incompressible in the scenario of horizontal flow in the x-y plane is that it ensures constant density throughout the fluid.