The easy way to think of it is essentially wave breaks up ducts (pipes, tubes, passages, volumes etc) into short segments.

These pieces each have the fluid mechanics equations solved across them for their give properties (ie the diameter of the duct is fixed for that section of duct). If you segment the duct into enough "elements" it enables the software to numerically solve the equation and creates a model for the entire network.

The 1D refers to the fact that each element only has one axis of fluid flow.