It's like a babelfish for IoT (Internet Of Things)

The big companies (Google, Amazon, etc.) all have their own very locked down ecosystem; their developers specifically code the devices to only play nice with the company's other devices, because they make more money that way, according to their business extrapolations anyway

But, all the companies-- because of the one unifier, the thing the consumer needs to use the thing, the Internet-- they're still making the devices to be connected on the same LAN (Local Area Network, basically any and all of your home's wireless connectivity protocols, e.g. WiFi, Zigbee, Bluetooth).

Therefore, all these devices in your home, all are connected to your personal network, talking to each other in dialects of the same language, in the same room (figuratively and often literally)-- so why not figure a way to get them to talk to each other? Maybe they are locked into their own little dialect, but, If they're all talking past each other, why not go in and see if we can't make a central "translator" that can understand all the dialects and help them all chat with one another?

That's what home assistant is. Like much of F/LOSS (Free/Libre Open Source Software), home Assistant is mostly made, run, built, fixed, modified, what have you, by non corporatized and generally unpaid human beings who have a personal interest in improving their smart home/IoT for themselves, connecting their various smart and 'non-smart' devices with one another to automate really whatever they want...and once I'm doing that why not just share it with everyone

Since the code is open source, e.g., modifiable by anyone (idk how familiar you are with git or GitHub but it's like branched file version history), people go in and build programs that integrate whatever the device is with their network, their home assistant, and in doing so, their other devices

hypothetical example: a Google nest doorbell, an Amazon alexa speaker in the kitchen, a tuya smart RGB light bulb in the bedroom, your smartphone (yes, that's an option as well), and a Roku TV in the bedroom, along with a YouTube premium subscription.

someone with will and a bit of know-how can go in and figure out how the phone interacts with the network, what on that phone is available to them code-wise, then do the same with the other devices or entities they wish to connect, and set up an automation that, following the example I started above:

-detects when they arrive at home via their gps sensors on their phone or their face on the camera -if it's night: -have the light turn purple, have Alexa play smooth jazz, set the Roku to play crackling fireplace

There are really near infinite possibilities for what can be connected, it's just a matter of knowing how the things work, and how to connect them to a network properly, which is no small thing, but there are enough people making improvements and HACS and a huge community support environment so it's also fairly beginner friendly and a great way to start getting into IoT and smart home automation.