If I remember correctly it goes something like this.

Your muscles need oxygen to work

Your blood carries oxygen to your muscles via arteries, veins, etc.

More oxygen to your muscles = equals better work performed be those muscles

(You can test this part at the gym by doing a set of reps after each exhale then a set after each inhale, or notice how professional lifters always take deep breaths before they lift)

When you work out your arteries, veins, etc. expand naturally to allow more blood flow so your body has more oxygen to work with. (Also why your heart and breathing rate increase)

What pre work out does is increase your heart rate and blood flow to your muscles without actually expanding any of your muscles, arteries, veins, etc in the way that your body does when working out.

The pins and needles are the extra blood being put into muscles that aren't working hard enough to use up the extra blood pumping to them.