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A process is, essentially, a running application. Each .NET application runs in its own process. If you have Word, Excel, and Visual Studio open, you have three processes running. If you open another copy of Word, another process starts up. Each process is subdivided into one or more application domains (or app domains). An app domain acts like a process but uses fewer resources.
App domains can be independently started and halted; they are secure, lightweight, and versatile. An app domain can provide fault tolerance; if you start an object in a second app domain and it crashes, it will bring down the app domain but not your entire program. You can imagine that web servers might use app domains for running users' code; if the code has a problem, the web server can maintain operations.