Pull-through PCR is a method to introduce restriction sites on the end of a PCR product. Many people will introduce their restriction sites on their original PCR primers, but this can sometimes cause non-specific binding or reduced PCR efficiency. The pull through method performs a PCR like normal and you purify the PCR product from a gel. From this PCR product, you THEN run a few additional PCR steps with primers that have your restriction sites on the ends.

This increases the likelyhood of these primers binding to your DNA target because now the only template is your PCR product. Its a way to increase the signal to noise essentially.

Hope that helps,

~Adam