The value/price of a coin is largely determined by its condition or grade, but grading a coin is fairly subjective. Over the past couple of decades, grading has evolved from verbal descriptions (About Good, Good, Fine, Very Fine, Extra Fine, About Uncirculated, Uncirculated, Brilliant Uncirculated - have I left any out? Proof is not a condition, rather a manufacturing process) to a numerical scale ranging up to 70 that allows a finer degree of grading. Still, at the present, grading is done by humans and is subject to differences of opinion. There are books that illustrate certain coins in many different conditions so an amateur can get a ballpark grade, but there are still many factors that contribute to different grades for the same piece.
Here is where the professional grading companies step in. They provide (for a fee, of course) a service where they will grade the coin (in hopefully a standard fashion) and encapsulate it in plastic so we can be assured that the grade corresponds to this particular coin (no switching coins). That way, the buyer, especially in long-distance transactions, has some degree of assurance that he/she is buying a standardized produce. The downside is that there are several companies grading and "slabbing" coins and they don't all have the same reputation. In fact, up until a year or so ago, there were coins on the market (especially ePay) that were encapsulated but the grading was not done by reputable graders. This caused ePay to specify the companies for whose products they would accept the term "slabbed".
I've seen many dealers buy slabbed coins which they think deserve a higher grade, pop open and discard the slabs, and submit the coins to a different grading company in hopes of obtaining a higher grade. Since there is often a vast difference in price between close grade numbers in high-value coins, the dealers figure the cost for having a coin re-graded is worth it.
eBay has tutorials on many subjects - take the time to read some of them. For instance,
http://search.reviews.ebay.com/_Coins-Paper-Money_W0QQucatZ11116QQuqtZg is where there is info on grading.
John in ID