They provide inverse operations when working with signals.
Analysis breaks a signal into simpler constituent parts.
Synthesis assembles a signal from its constituent parts. https://youtu.be/gZNm7L96pfY
This view can be further abstracted to other domains where complexity exists. Analysis decomposes the complex into elements that can be individually manipulated. Synthesis combines these back to a to complex form.
Both stages are important, but when used in tandem provide the ability to reason about, act on, and produce the style of complex information that defines real-world problems.