I started using HA to turn lights on and off on timer while I'm out of town, so it looks like the house is occupied.

Then, because I am a nerd, I added some environmental sensors so I could see temperature & air quality.

Eventually linked the air quality sensor to a smart thermostat, so it could turn the HVAC fan on when the air is dirty & off when clean, rather than leave it on 24/7 (like the HVAC people recommend) or on 'circulate.' That saved around 3.5 kWh electricity every day, or $100/year, while keeping the house dust and allergen-free.

Lots of things can be hooked up through it. One of the biggest things I find I like about it is the way you can merge ecosystems with it.

At home with HA I have an LG TV, Philips Hue lights, a Tapo vacuum cleaner, my EV charger, my own home made solar hot water system controller, a presence sensor that also does CO2 and temperature, a hot tub, and a few other bits and pieces. All of which can be viewed and controlled in the one interface, not the 6 or 7 apps that every individual device wants me to install.

But automations and notifications are the big thing. The presence sensor in the living room turns off the tv if nobody is in front of it for more than an hour. The EV charger tells me when the car is charged. An hour before sunset the light in my living room slowly dims on, and dims off after 9pm when the presence sensor says there's nobody around. When my solar hot water system is a bit slow to heat up on a cloudy day, I get an email telling me to turn the electric booster on (and off when the water's hot). Every Tuesday and Thursday evening the vacuum cleaner is set to clean the living areas, but it doesn't if someone is watching tv, as detected by the presence sensor and the television.

I also don't have to get off the couch to turn on a light, but the idea is that you set up automations that do all the button-pressing for you.

First off, I don't get why someone down voted you for just asking a question... So take my upvote.

There is so many things you can do with home assistant therefore not easy to explain all possibilities, here are a few things that comes to mind.

Many smart home users prefer to not depend on cloud giant and that's a way to keep it local and keep everything in just one app even if devices are not same brand. It can just trigger light automatically depending of scenarios (if you have earring issue, it can trigger some light when someone rings at the door). You could have switch that are not well placed and are not practical and it enables you to add wireless switches elsewhere. It can also monitor appliances (and/or services) so it can remind you stuff (useful for some people that easily forget things) like emptying washing machine, taking trash out... (No need to add many daily reminder in your agenda which would have single notification that you will wipe out and forget). You can add security cameras and keep them local only. It can remind you to close windows when you just left home or because it started raining. It is also a way to monitor for exemple water leaks so you can react quicker to avoid big damages (imagine a small leak behind a sink which you wouldn't notice for quite sometimes) same thing applies for smoke detectors, CO2 levels...

The list of things it can do is really endless.

In essance it lets you put every single smart thing/sensor/connection into a single place for manipulation.

It can be to avoid getting out of the couch to turn on a switch. (In my case pausing music and dimming lights when the TV turns on)

It can also be watering your veggie garden based on a combination of soil moisture and daily forecast.

It can also be having a button linked to your car screen and your watch that opens the garage door; but only if your child isn't napping in the room directly above the garage, and someone is detected to be at or near home.

It can also be automating your toddler's evening cool down routine for bed (slowly dimming lights, turning on sound machine, playing lullabies).

It can also play "The Wiggles - Bin Night" at 18h15 the night you need to take out your garbage, then follow up with a voice to text of what bins need to go out.

It can also be a morning automation tool to start the coffee machine and play the news and music.

It can also turn up/down the thermostat when it detects you leaving work, but cross referencing if there is an activity in the calendar with a different location first to analogously estimate if you aren't coming home. Then start the thermostat after you leave that location with a time lag based on the method of transportation used to get an ETA (did I travel by car, bike, or bus? Determine then get an ETA)

And if you happen to like chickens it can do stuff like this:

https://www.reddit.com/r/homeassistant/comments/schcw0/diy_smart_chicken_coop_and_inapp_egg_counter/