Linux systems provide a variety of system services (such as process management, login, syslog, cron, etc.) and network services (such as remote login, e-mail, printers, web hosting, data storage, file transfer, domain name resolution (using DNS), dynamic IP address assignment (using DHCP), and much more).
Technically, a service is a process or group of processes (commonly known as daemons) running continuously in the background, waiting for requests to come in (especially from clients).
Linux supports different ways to manage (start, stop, restart, enable auto-start at system boot, etc.) services, typically through a process or service manager. Most if not all modern Linux distributions now use the same process manager: systemd.