Relay notifications or/and messages, and other useful functions, like automated control of your home server and other electronics like vacuum robot and such from places with bad connection, also automated fetch of information you need, like timesheet or news you follow or state of your home and this is just fraction of use cases the only limiter is your imagination
You can do this through almost any messenger, if you like open source then matrix will be your choice, people use telegram because it is unblockable, some countries tried to block it and failed which proved telegram efficiency, for example if you go to country where most of internet inaccessible due to various reasons, not only blocking, I'd use telegram to remotely control my home server and fetch data i need and will use software called browsh to browse internet, creator of browsh told himself that idea came to him when he travelled do tibet and internet connection was limited to 5kb/s, also terminal apps to browse YouTube and download everything with aria2c, yt-dlp, gallery-dl
It's very effective for sysadmins if you want to get real time notifications about server stats. The possibility are endless because you could push everything with curl from commandline or cron. For example why not get informations about SSH login attempts or CPU usage or unattended upgrade logs?