Google Cloud Composer is a fully managed workflow orchestration service, built on Apache Airflow, that empowers you to author, schedule, and monitor pipelines that span across clouds and on-premises data centers.
Cloud Composer is a product of Google Cloud Platform (GCP). It is essentially "hosted/managed Apache Airflow."
The product allows you to create, schedule, and monitor jobs, each job being represented as a DAG (directed acyclic graph) of various operators. You can use Airflow's built-in operator definitions and/or or define your own in pure Python.
While technically you can do data processing directly within a task (instantiated operator), more often you will want a task to invoke some sort of processing in another system (which could be anything - a container, BigQuery, Spark, etc). Often you will then wait for that processing to complete using an Airflow sensor operator, possibly launch further dependent tasks, etc.
While Cloud Composer is managed, you can apply a variety of customizations, such as specifying which pip modules to install, hardware configurations, environment variables, etc. Cloud Composer allows overriding some but not all Airflow configuration settings.
Further technical details: Cloud Composer will create a Kubernetes cluster for each Airflow environment you create. This is where your tasks will be run, but you don't have to manage it. You will place your code within a specific bucket in Cloud Storage, and Cloud Composer will sync it from there.
Airflow documentation: https://airflow.apache.org/docs/stable/
Cloud Composer documentation: https://cloud.google.com/composer
