A functional language doesn't (in general) rely on mutating a variable. Because of this, we don't have to protect the "shared state" of a variable, because the value is fixed. This in turn avoids the majority of the hoop jumping that traditional languages have to go through to implement an algorithm across processors or machines.
Erlang takes it further than traditional functional languages by baking in a message passing system that allows everything to operate on an event based system where a piece of code only worries about receiving messages and sending messages, not worrying about a bigger picture.
What this means is that the programmer is (nominally) unconcerned that the message will be handled on another processor or machine: simply sending the message is good enough for it to continue. If it cares about a response, it will wait for it as another message.
The end result of this is that each snippet is independent of every other snippet. No shared code, no shared state and all interactions coming from a a message system that can be distributed among many pieces of hardware (or not).
Contrast this with a traditional system: we have to place mutexes and semaphores around "protected" variables and code execution. We have tight binding in a function call via the stack (waiting for the return to occur). All of this creates bottlenecks that are less of a problem in a shared nothing system like Erlang.
EDIT: I should also point out that Erlang is asynchronous. You send your message and maybe/someday another message arrives back. Or not.
Spencer's point about out of order execution is also important and well answered.
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