When you replace a card what does that mean?

When some cards say to replace a card what does that mean? Can you replace it with any card of your choosing? 

I think it just means to put that card back where you got it. For example, look at the top card of a deck then replace it (put it back on top). 

Yup, that's what it means :). Replace as in "put it back", not "put something else there instead".

You literally just re-place it. You place it, again. I think they could have been more concise with "put it back," but whatever.

Then you need a deck manipulator if it isn't a useful card. Either to move it to trash or the bottom of the deck.