In a lot of all-grain brewing systems, there's a hot liquor tank which basically just functions as a place to heat your water. As soon as the water is heated, it's drained into the mash tun which has the grain in it.
Why not just heat the water in the same tank as you mash in? It seems like a huge inefficiency to have another tank just to heat water in.
There are two answers, depending on size:
In largish setup, you may want to be able to heat water for second batch when you are mashing first one.
To heat water fast, you want heating element to output a lot of power. It could burn your mash if used in the tank with grain. It is easier and more reliable to switch heater on full for 10% time than on 10% power continuously. That's your reason for smaller installations.
In both situations, precise transfer of water is easier than transport of grains. If you put grains in the tank first, you can close it and use hot water pump to add hot water. No risk of spills landing on brewmaster. No open doors to cool your mash.
Now imagine adding grain to hot water. You need bigger opening, so water cools in the process. Waste of energy. And safety risk at the same time.
All that being said, one tank systems exists and have their own merits. Both kinds make sense, for people who need specific upsides and can live with specific downsides of each way.
One tank systems exist, mainly at a homebrew level. They are used for full volume mashes, BIAB (Brew in a bag, an unfortunate name), eBIAB and other electric recirculating mashing systems like Grainfather. Many, many homebrewers have adopted BIAB systems for ease and single vessel mashing. It doesn't scale up well for a commercial brewery, at least for traditional BIAB systems because of the weight of the mash when you pull the bag. But they do exist.
Why not just heat the water in the same tank as you mash in? It seems like a huge inefficiency to have another tank just to heat water in.
You could heat water in your mash tun, providing it was a kettle with a false bottom (as opposed to a cooler with a false bottom) a then add grain, but then you would still need an external way of heating your sparge water.
In a basic batch-sparge system, the reason for the hot liquor tank is gravity. Your hot liquor tank (which is a misnomer, really a hot water tank) is the highest container, so you can use gravity to rack to your mash and lauter tun, then gravity again to rack to your boil kettle.
I use a very rudimentary, batch sparge system, with one tun (a 10g igloo cooler with a temperature gauge and a valve), one burner, one kettle (8g with temp gauge and valve) and a few buckets. I have to swap elevations of the kettle and tun each time I want to transfer and I cannot transfer my mash to my kettle since I need it to heat up my sparge water. I have to rack it to a bucket, then rack the bucket to the kettle after I'm done transferring my sparge water to the tun.
I've thought about another kettle, burner and tun, but not for a gravity system, so I can do two 5 gallon batches in parallel.
You can also heat your strike and sparge water in your kettle, provided you are happy to either sparge into a holding tank, or do a no sparge lauter. Generally speaking, unless you're single vessel brewing, the HLT is for convenience. It's not necessary, but adds a boatload of flexibility to your system.
We heat the strike water in the boiler. Mash in the cool box type mash tun. Heat sparge in boiler. Drain wort into fermented. Check volume and adjust sparge if needed. Run sparge into mash tun. Pump wort and sparge into boiler. Start boil.
