Why might threads be considered "evil"?
What makes threads "evil" is that once you introduce more than one stream of execution into your program, you can no longer count on your program to behave in a deterministic manner.
That is to say: Given the same set of inputs, a single-threaded program will (in most cases) always do the same thing.
A multi-threaded program, given the same set of inputs, may well do something different every time it is run, unless it is very carefully controlled. That is because the order in which the different threads run different bits of code is determined by the OS's thread scheduler combined with a system timer, and this introduces a good deal of "randomness" into what the program does when it runs.
The upshot is: debugging a multi-threaded program can be much harder than debugging a single-threaded program, because if you don't know what you are doing it can be very easy to end up with a race condition or deadlock bug that only appears (seemingly) at random once or twice a month. The program will look fine to your QA department (since they don't have a month to run it) but once it's out in the field, you'll be hearing from customers that the program crashed, and nobody can reproduce the crash.... bleah.
To sum up, threads aren't really "evil", but they are strong juju and should not be used unless (a) you really need them and (b) you know what you are getting yourself into. If you do use them, use them as sparingly as possible, and try to make their behavior as stupid-simple as you possibly can. Especially with multithreading, if anything can go wrong, it (sooner or later) will.
Simple answer the way I understand it...
Most threading models use "shared state concurrency," which means that two execution processes can share the same memory at the same time. If one thread doesn't know what the other is doing, it can modify the data in a way that the other thread doesn't expect. This causes bugs.
Threads are "evil" because you need to wrap your mind around n threads all working on the same memory at the same time, and all of the fun things that go with it (deadlocks, racing conditions, etc).
You might read up about the Clojure (immutable data structures) and Erlang (message passsing) concurrency models for alternative ideas on how to achieve similar ends.
When people say that "threads are evil", the usually do so in the context of saying "processes are good". Threads implicitly share all application state and handles (and thread locals are opt-in). This means that there are plenty of opportunities to forget to synchronize (or not even understand that you need to synchronize!) while accessing that shared data.
Processes have separate memory space, and any communication between them is explicit. Furthermore, primitives used for interprocess communication are often such that you don't need to synchronize at all (e.g. pipes). And you can still share state directly if you need to, using shared memory, but that is also explicit in every given instance. So there are fewer opportunities to make mistakes, and the intent of the code is more explicit.