It's not directly a PowerShell issue. When a using block terminates, the specified object(s) have their Dispose() methods called. These typically do some cleanup operations, often to avoid leaking memory and so forth. However, Dispose() doesn't delete the object. If a reference to it still exists outside the using block (as in this example), then the object itself is still in scope. It can't be garbage-collected because there's still a reference to it, so it's still taking up memory.
What they're doing in your example is dropping that reference. When powershell is set to null, the PowerShell object it was pointing to is orphaned, since there are no other variables referring to it. Once the garbage collector figures that out, it can free up the memory. This would happen at the end of the method anyway (because powershell would go out of scope), but this way you get the system resources back a little sooner.
(Edit: As Brian Rasmussen points out, the .NET runtime is extremely clever about garbage collection. Once it reaches the last reference to powershell in your code, the runtime should detect that you don't need it anymore and release it for garbage collection. So the powershell = null; line isn't actually doing anything.)
By the way, this pattern looks very strange to me. The usual approach is something like this:
using (PowerShell powershell = PowerShell.Create())
{
//...
}
This way, powershell goes out of scope at the end of the using block, right after it's disposed. It's easier to tell where the variable is relevant, and you save some code because you don't need the powershell = null line anymore. I'd even say this is better coding practice, because powershell never exists in an already-disposed state. If someone modifies your original code and tries to use powershell outside the using block, whatever happens will probably be bad.