Took me a moment but I get exactly what the OP means...happens to me now and then.
On a website for example if you accidentally touch an area the entire area (a block of text for example) will be highlighted with a blue overlay, the same blue overlay that would highlight a single word to allow you to copy it. Usually it requires touching the specific area three to fours times. It's great if you want to copy that entire area, but annoying if you only meant to move the page, etc. The "feature" won't work on everything, it depends on how the document or website is built. It works best with documents, but will work on some websites.
In any case, it's a matter of touch. Resting your fingers or touching the screen in just the right way...so that the iPad thinks you want to copy an area is what causes it. If it happens generally touching an area outside of the highlight removes it.
Best advice is to simply be a little more careful how and when you touch the iPad's screen.
I don't know of any way to turn the copy feature "off" though.
I'm moving this to the help section for those that follow.