Businesses have clients and servers have clients. In both instances, there exists a one-to-many relationship. Just like a business may have several clients, a server can communicate with multiple clients. In computer networking, this is called the client-server model.
A client is any device that communicates with a server. It may be a desktop computer, laptop, smartphone, or any other network-compatible device. In a home network, "smart" devices, such as Wi-Fi-enabled thermostats, lights, and appliances, are considered clients. In an office network, systems that access files from network-attached storage are clients of the file server. Most networks allow client-to-client communication, though the data flows through a central point, such as a router or switch.
On a larger scale, whenever you access a website, your device is the client, and the web server hosting the website is the server. From a software perspective, your web browser is the client software and the program that responds to requests on the web server (Apache, IIS, etc.), is the server software. Similarly, when you check your email, you connect to a mail server. Your device is a client of the mail server, and your email program or webmail interface is the client software.