Most CPUs these days are multi-core. Put simply, that means they have several processors on the same chip.
If you only have a single thread, you can only use one of the cores - the other cores will either idle or be used for other tasks that are running. If you have multiple threads, each can run on its own core. You can divide your problem into X parts, and, assuming each part can run indepedently, you can finish the calculations in close to 1/Xth of the time it would normally take.
By definition, the fastest algorithm running in parallel will spend at least as much CPU time as the fastest sequential algorithm - that is, parallelizing does not decrease the amount of work required - but the work is distributed across several independent units, leading to a decrease in the real-time spent solving the problem. That means the user doesn't have to wait as long for the answer, and they can move on quicker.
10 years ago, when multi-core was unheard of, then it's true: you'd gain nothing if we disregard I/O delays, because there was only one unit to do the execution. However, the race to increase clock speeds has stopped; and we're instead looking at multi-core to increase the amount of computing power available. With companies like Intel looking at 80-core CPUs, it becomes more and more important that you look at parallelization to reduce the time solving a problem - if you only have a single thread, you can only use that one core, and the other 79 cores will be doing something else instead of helping you finish sooner.