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Static IPs are mainly useful when you want to reliably reach devices in your network. If you want to remotely control a NAS, a printer, or a camera, for example, you need a fixed address - otherwise you'll assign the device a new address tomorrow and your connection will go nowhere. Static IPs are also practical for port forwarding to the outside world: without one, you'd have to constantly adjust your router settings if the address changes.
You notice this especially in everyday life with smart home devices or when you want to access home network stuff from outside. To be honest, for a standard PC or smartphone that just browses the internet, you don't need it - DHCP works perfectly fine for that. But as soon as you're building home automation or multiple devices need to communicate with each other, a static IP (or at least a DHCP reservation on the router that treats the device the same way every time) becomes essential.
The extra effort is tiny: you either configure the IP directly on the device itself, or - and this is more elegant - you tell the router to always give certain devices (identified by their MAC address) the same address. Then you just need to think through your network once, decide which devices should be static, and after that it runs reliably.
Do you only need it for specific devices that have to be reachable at all times - like servers, printers, NAS, stuff like that - or are you asking more out of general interest? In everyday use, a static IP mainly gives you reliability, because your device won't suddenly get a new address and then services go down or port forwarding stops working. Without a static IP, you constantly have to check what address your device currently has whenever you want to reach it from outside.
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