What is per e.g Hydrogen PERoxide?

I can`t quite make 100% sense of your question, but Hydrogen peroxide (H2O2) is basicly water with an extra oxygen atom attatched to it.

it`s a reasonable powerfull oxidising agent at high concentrations too

Per in Hydrodgen per oxide

Per in various other copunds e.g Potassium permaganate

 

Why is it PER oxide and not just hydrogen oxide

It's just remnants of an old prefixing system.... -ite -ate per- -ate, same with -ides

The oxygen in the peroxide has a different oxidation number (it's not -2). Try figuring it out for yourself

'per' refers to an ion species with one more oxygen atom than its 'ate' species.

 

http://chemserv.ventura.cc.ca.us/doliver3/chem20/chap06.htm