Roughly speaking, hands with good visibility are the ones that will let you know where you stand with your hand.  You might be ahead or behind, but point is, you can see that clearly.  Hands with poor visibility won't tell you much about this; you might be ahead or behind, but you won't know that for sure.

In general, hands that have nut potential (or nut blocker) tend to have good visibility, because once you hit the gin card, you will know that you either have the nuts, or block the nuts so that your opponents can't have it.  On the other hand, if you have a 4th nut flush draw on the flop OOP and nothing much else, you have a poor visibility because even if you hit the flush on the turn or river, you won't know where you are exactly.  Against most value betting range, you have a weak bluff catcher, and you probably can't value bet confidently in most cases.

An important thing about visibility is that, hands with better equity don't always have a better visibility.  Let's say, the flop is J96ss and you are facing some heavy action with a) AK53ss (NFD) and b) 66xx with no redraw.  It is possible that you have more equity with 66 than AK53ss against his strongish flop range, but AK53ss gives you a much better visibility.  

Because of all this, visibility gives you a reason to continue on flop more often (but not always) with nutty hands, and less often with non-nutty hands.  Also, to a lesser extent, this applies to preflop hand selection.  For example, AKJ6 with nut suit is a far more playable hand than AKJ6 with K high suit in a MW pot.  Last but not the least; visibility tends to matter more when you are OOP, but this is not to say that you can completely ignore it when being IP. 

I'm sure there are a couple more important stuff that I haven't covered, but I'm feeling a bit sleepy now :)  Feel free to ask questions! 

Flop is J 9 6 with two hearts. 

You check-raise 6644ss (no hearts) heads-up after calling a raise in the big blind. Villain calls.

Now think about how the turn and river will play out. You have low visibility because the board will change a lot by the river, and many draws will come in. But you don't cover any of them, and you don't know which hit Villain, and you have to act first.

You then find yourself regretting that c/r. Because building big pots with poor visibility and stacks behind sets you up for guessing in big pots later. Good thing to avoid.

Ok I think I get it now.Thanks a lot for clearing that up for me. I have a few questions though. So is visibility a concept that is relevant only really to dynamic board textures? Also is their any link with the skill level of the player i.e. is a more skillful player going to have better visibility in certain spots or are we just putting that under the category of hand reading? Thanks again for answers.

visibility = being in position + drawing to the nuts (for example Nut Flush Draw, or nut straight draw in rainbow flop). I

visibility in PLO is (imo) the main reason that position is so important.  The second reason would be preflop equities.

In PLO when I play out of position I often feel lost in a fog of decent equity and bad turn cards.  When I play in position I see clearly while my opponents stab around in that fog.