A "core" represents an actual physical subset of a processor that can by itself handle processing, whereas a "thread" is how many actual processes the processor can handle at once. Intel has developed a technology they label "hyper-threading" this technique allows for one physical core (which would normally only be able to handle one thread at a time) to now be able to handle two threads simultaneously.
A thread is a task that the processor must handle, for a simple explanation, you can assume that every application you open (such as paint, notepad, media player) has its own thread... now this does not mean you can only open 2 applications at once, simply because the processor and OS work so fast at 'switching threads' to handle the needs of every application that you have open. You will just experience better performance with more cores because now you can dish out all of the work to more core processors.
For example, my work computer has an i7 in it. The i7 has 4 physical cores, but each core can do 'hyper-threading' which allows this processor to handle 8 threads at once. So if I open up the task manager, I will see 8 boxes for processor performance scale.
A general rule of thumb is that more physical cores are better than more threads. So if you were comparing a processors that had 4 cores and 4 threads, would be better than 2 cores 4 threads. But the more threads your processor can handle, the better it will perform while multitasking and for some very intensive applications (video editing, CAD, CAM, Compression, Encryption, etc) will in itself utilize more than one core at a time.