Rocker is the amount of curve to the bottom of the board. A quick and (really) dirty way to measure the effective rocker on a board that uses a fin system is to remove the fins, lay it on a level floor and apply a ruler to measure the distance between the bottom of the nose or tail to the floor. There are more accurate ways of doing this measurement but for for the sake of discussion this cheater method will usually get you close enough.
When most surfers think of rocker they fixate on nose rocker and relate that curve to their ability to make a critical drop in a steep wave without pearling. But that's just the beginning. In conjunction with the curve of the outline of the board (aka planshape) a board's rocker will also greatly affects how loosely it will turn, how and where the board will drive through a turn, and how the board will paddle.
The other thing that many surfers don't realize is that, except for the noseriders, the amount and type of tail rocker in a board has more effect on how the board will surf for most people than the nose rocker.
Everything else being equal and in general, a board with a flatter rocker will paddle faster and with less effort than a curvier rocker. It will set into trim more easily but be harder to break out of trim and harder to turn. It will pick up a soft wave more easily but in a faster wave it will be much less forgiving with respect to making the transition from paddling to surfing - the balance point is further back and more of the volume has to get past the peak before that balance point will engage. In other words, you have to paddle further into that wave before the board will pick it up and in doing so you are reducing the length of time you have to pop up and control the tail.
The amount of rocker that will work best for you depends mostly on what you're trying to do.
What conditions do you intend to use the board in? This refers both to the speed/shape of the wave as well as the size of the wave.
Are you trying to use the board in all conditions or do you intend to use it as part of a quiver of more specialized boards?
What kinds of turns do you expect or aspire to pull off on that board in those conditions?
What's your timing like with respect to making the transition between paddling and surfing?
What's your paddling like? This refers both to your endurance and your sprint speed.
What's your skill level with respect to finding the optimum stance for your board when considering its fin setup and rail configuration?
If you generally do okay with respect to your paddling, transitions, and your position on the board relative to its fin/planshape setup then you have more latitude to match your rocker with your wave shape/speed. If you're struggling with those elements then you have less latitude, which usually means you're going to need more rocker. If you're trying to surf the board more vertically then you're going to need more rocker whereas if you're going for the longer drawn out carves you're going to want less rocker.
If you surf a longboard (either traditional or performance) OR if you are looking to surf the high performance boards modeled after what the pros use then finding a board with the optimum rocker won't be a problem. Your local McSurf Superstore is full of those.
If you're looking for one of the alternative shapes like the fishes or eggs or funboards or "wider" performance boards then it can get a little tricky because most of the contemporary surfboard blanks have a lot of rocker relative to their lengths. That's good if you take after Kelly or Taj but it's bad if you take after any of your heroes from the 1970s or 1980s.
If the latter applies to you then this is where you might be better served by skipping the shop boards altogether and hooking up with a custom shaper who is in a position to either order a blank with a custom rocker or else choose an oversized blank that has your target rocker buried somewhere in the middle.
In general and with the notable exception of the longboards, I don't think most surfers - including most older surfers - need nearly as much rocker as they've been buying. If you're over 50 and you've been surfing for a long time then you probably don't have a problem with your transitions or with pearling, and you're probably not trying to blow the tail out of the water or launch an aerial.
On the upper end I like to apply the Mark Richardson filter to surfers. If someone can outsurf what MR was doing on his twins back in 1978 then they probably have use for the curvier rockers and thinner foils. If they can't outsurf MR circa 1978 then chances are pretty good that they don't need any more rocker or any less volume than what he was using.
The prevailing wisdom among aging boomers is that there are no flattering pictures of us from the late 1970s or the early 1980s. However, there were a lot of great boards back then. This is demonstrated by the modern revival of those general designs, the application of new-skool logos and fin systems notwithstanding.