Hyper-Threading is not that complicated to understand, on a CPU that does not support Hyper-Threading you are only able to process one thread at a time. Due to the fact that your system is always running multiple threads it would give you a big improvement if you could process more then one thread at a time. The way Hyper-Threading works is because your processor rarely uses all of its resources, the one processor you have in your system is split in to two logical processors. Let's look at some visual aids that may be able to explain this better.

As you can see in the photos above each logical processor takes up part of the system resources. With the Pentium 4 the first logical processor is the main processor and takes up as much of the resources as it needs and the second logical processor uses whatever is left. Let's look at another visual aid.

The picture above shows the CPU usage at 12% this leaves 88% of your CPU's resources wasted. What Hyper-Threading does is uses another logical processor to take advantage of this wasted space. With the ability to be able to run 2 threads per clock cycle your performance in some cases will improve but it depends on the program that you are using and the strain that the first logical processor is under.

Performance Acceleration technology (PAT) provides more performance by optimizing memory access between the CPU and memory on 800MHz FSB and Dual channel DDR400 configurations. The only chipset to use (PAT) is the i875P and to use it you have to be using an 800MHz FSB CPU and 400MHz Dual channel memory. This technology can reduce up to two clock cycles from any given process. According to Intel some motherboard manufacturers are advertising their i865PE chipset based boards with PAT but these platforms are not intended to use PAT and in some cases cause stability problems according to Intel.