The grading system of white water is a largely subjective affair, but I will do my best to give what is normally conceived to be meant by the grades I (the easiest) to VI (verging on suicidal) from a kayaker's perspective, although it will apply roughly the same to rafting teams. It is probably worthwhile to give a short description of river features as well - these are the obstacles you find on a white water river that must be negotiated, and generally these become larger and more frequent the higher the grade.
First though a mention of two terms - scouting and safety. Scouting is the act of getting off the river before a large feature such as a high-grade rapid, drop or siphon (see below), normally where it is no longer possible to see from sitting in your boat the next place you could find an eddy that has line of sight to your group. Unless you are certain the river does not have anything dangerous to throw at you, run nothing blind (and even then be very cautious). Safety does what it says on the tin. Often after scouting it will be necessary to set up safety teams to protect sections of the river where people are likely to make mistakes. Swimmers (referring to people who have fallen out of their kayak after capsizing and being unable to roll, not nutters swimming down white water!) are likely to need rescue quickly, and being in a good position to get a rope or a live bait to a swimmer could be the difference between life and death.
So, river features:
EDDIES: are areas of slack water that form behind rocks and other obstructions to the water, allowing a kayaker to take a break from paddling in the main flow.
HOLES: are formed where the water goes over a small drop and curls back on itself off the river bed. This produces a 'towback' effect, that can suck kayaks upstream and into the hole, where they may be forced to either surf the wave that forms or be capsized by the force of the water. On higher grades this process can repeat itself until the paddler bails and either manages to swim down and out, or is recirculated until they either drown or are rescued. On low grades holes can be simply ploughed straight through. On moderate grades (4-5) holes can be avoided by 'boofing' - launching the kayak off the drop so that it lands flat and maintains its speed. On the higher grades holes are to be avoided at all costs!
SLIDES AND DROPS: are fairly self explanatory. A slide is a rock or man-made slide over which the water runs and kayaks can slide down. Because the water is never very deep, control is somewhat difficult as you descend. Drops are waterfalls of anything from a couple of feet to, well, 186ft is the highest that has ever been run, a feat recently undertaken on Palouse Falls by a man called Tyler Bradt. When running a large drop angle is the key - if you land flat you can break your back.
SIPHONS: are incredibly dangerous - slots in the rock where the water goes underground or disappears underneath large boulders without leaving enough room for a kayak to go through. Go down a siphon and you're pretty much dead unless you happen to get stuck with your head out of the water in which case it may be possible to rescue you before the force of the water crushes your boat. Generally though these do not appear except on high grades and can often be avoided fairly easily.
PINS: not strictly a feature, pins are where your boat is pinned violently against a rock by the force of the water. Often they happen so fast that you cannot do anything to react, and they can put you vertical, sideways, or upside down without necessarily any hope of escape. They can normally be avoided though if you steer clear of rocks, although this is easier said than done.
STRAINERS: are normally in the form of fallen trees that have blocked part of the river. If the flow is not too serious then these can be ducked under with care, but on larger rapids and drops must be avoided at all costs as, once again, if you become trapped underneath that could be the end of you!
I make white water kayaking sound like the most deadly thing in the world. However, with experience and care serious white water rivers can be run with minimal risk. And if there was no risk, then where would the fun be?! Anyway, on to the grading system:
Grade I - The current is fast with a few minor obstructions and small waves, but these are easily negotiated. In the unlikely event of a swim, the bank is easily reached, although the river tends to be fairly wide.
Grade II - Rapids are straightforward with obvious channels that do not require scouting, and few rocks that are avoided easily enough using basic paddling strokes. There will be a few small drops and waves but nothing that poses any great danger even to largely inexperienced paddlers. Swimmers need to be strong but are unlikely to be injured.
Grade III - Rapids are large and irregular, with powerful currents, eddies and waves. Although it will require a good deal of skill to negotiate the rapid entirely unscathed it will not be difficult for an experienced paddle, and scouting is only really necessary for the least experienced paddlers. Rescue and scouting is normally quite easy, although there is a considerable risk of losing equipment in a swim. Swimmers need to either be very strong, have good knowledge of how to swim in white water or get rescued from the bank.
Grade IV - Rapids are large and very powerful but generally predictable. There are constricted passageways and unavoidable waves and holes. Fast, skilled and strong control of the boat is required, and scouting is strongly recommended as many rapids require "must moves". If you don't make a must move, they are downgraded to "seriously recommended moves" and as swimming is quite dangerous a strong Eskimo roll is imperative. Self-rescue is near-impossible so well trained safety on the banks is imperative. Poor choice of line or a failure to boof will create a serious risk of being recirculated in the larger holes. A decent creek boat and helmet with ear protection is recommended.
Grade V - Rapids are bordering on the suicidal, with extreme power and huge features with vast towbacks that can recirculate a swimmer indefinitely. Eddies are normally small, turbulent and difficult to reach, meaning stretches are usually run in one big panicky adrenaline rush, and scouting is difficult but nevertheless imperative in order to survive. An invincible Eskimo roll, high quality equipment, serious experience and a high level of fitness are required to survive. Swimming is extremely dangerous and rescues often near-impossible.
Grade VI - Rapids are so large, full of sharp rocks and immensely powerful that a successful run even by an incredibly experienced, fit and well equipped paddler is still based largely upon luck. Very few people have ever paddled these rivers, if indeed any, as the consequences of a small error are likely to result in death. Only an elite team with extensive safety preparation, detailed scouting, perfect conditions and a disregard for their own safety should even consider attempting such a rapid.
Enjoy your paddling!