Building on Jon Skeet's reply, there are times when you want to invoke a delegate and wait for its execution to complete before the current thread continues. In those cases the Invoke call is what you want.
In multi-threading applications, you may not want a thread to wait on a delegate to finish execution, especially if that delegate performs I/O (which could make the delegate and your thread block).
In those cases the BeginInvoke would be useful. By calling it, you're telling the delegate to start but then your thread is free to do other things in parallel with the delegate.
Using BeginInvoke increases the complexity of your code but there are times when the improved performance is worth the complexity.