In my experience overlapping PCR can mean one of two things:
1. Design primers for your DNA region that have overlapping primer sites. For example, if you want to amplify a 2 Kb sequence with 2 primer sets, primer set A may amplify from position -100 to 1,100 and primer set B might amplify from 900 to 2,100. Your overlapping sequence would be the 200 bp between 900 and 1,100. I generally only do this if I need the sequence that might be under one of my primers or for RD cloning.
2.. Design more than one forward and reverse primer over the region you wish to amplify to ensure that you get at least one PCR amplification product. This is done when you might have polymorphisms you cannot avoid under your primers.
I hope this helps, I'm sure that there are other examples...
Generally when I do overlapping PCR it is in order to ligate two things together that I want to combine. For example, if I'm working with a strand that has a pCAG and another with a TetOn3G, I could combine these two, given the right primer design strategy, using overlapping PCR. The final product would need to be gel run with a marker though, in order to extract the band that matches your expected product kb size.
"Overlapping PCR is a common technique used by molecular biologists in various fields that allows the user to ‘stitch’ together various individual DNA fragments. Some of the applications of overlapping PCR include gene synthesis by assembly PCR, reporter gene fusion using GFP or RFP based fluorophores, and detection experiments through techniques such as loop-mediated isothermal amplification (LAMP)... "
Thanks for the extra input. I'd call the technique above stitching. My "definition" is more biased towards clinical applications where you wish to avoid allele drop outs.