ECM what is its purpose

Do you mean you're looking to buy something? A used what? Vehicle or computer? The ECM is the Engine Computer, (Engine Control Module). It calculates fuel requirements, controls the injectors and spark plugs, and sends data to the other computers. Typically they're bolted to the body and have one or more really big electrical connectors. There's dozens of problems that can be caused by this computer. It is one of the more misdiagnosed items, meaning it gets blamed for everything that can't be figured out.

If someone puts in an ad, "all it needs is, ... ", you can be sure it doesn't. If they correctly diagnosed it as such, they would have repaired it themselves to increase the vehicle's value, or they would not be selling it. They're selling the vehicle because they gave up trying to figure out the problem, or they determined it is going to be too expensive to repair.

Hello, I'm Danny
The pcm (powertrain control module) controls all the computer components and drivetrain components on your vehicle. It's not very hard to replace. The pcm is located on the right side of the firewall under the hood. If you purchase a new or used pcm it will have to be programmed to your particular vehicle. They usually run $250-1000 dollars depend if purchasing new or used plus programming. I've attached pictures below showing its location and how to remove/replace. Hope this helps and thanks for using 2CarPros.