A distributed system, in simple terms, is a collection of interconnected devices or processors that communicate with one another to accomplish a common objective. Essentially, it is an infrastructure of resources that function as a single entity and appear to the user as a single platform.

In a distributed system, tasks are divided into individual sub-tasks, which are then distributed among a network of computers, servers or storage devices, known as nodes. These nodes then work concurrently to complete the entire task. Distributed systems are used in various fields, including finance, healthcare, transportation, and entertainment, to name a few.

One common example of a distributed system is a cluster computer. It is a collection of individual computers or nodes that work together to accomplish computational tasks. In the case of cluster computers, the main objective is to provide greater computing power than a single machine, as well as support a higher level of availability, scalability and reliability.

Distributed systems are often used to perform complex computations such as data processing, machine learning, and artificial intelligence. For example, the Google search engine is a distributed system that performs complex computations across several nodes to provide relevant search results to a user.

Scalability is an essential property of distributed systems. As the number of nodes increases, a distributed system can accommodate more computational requirements, providing greater processing power and storage capacity.

One of the main challenges associated with distributed systems is their complexity. The distributed nature of these systems means that they are largely decentralized, making it hard to ensure complete system control. Additionally, security and protection of data are paramount due to the distributed nature of the system. Thus, managing communication between nodes and coordinating data in a distributed system can be challenging.

In conclusion, distributed systems have become a significant part of modern computing. They offer improved performance, scalability and reliability. They are integral to numerous essential functions of our society, from finance to healthcare. Nevertheless, as the handling of the immense amount of data in distributed computing requires an unavoidability of distributed systems, several challenges must still be overcome, including security, performance, and collaboration.