A SYE is a slip yoke eliminator...but it is an incorrect term for what is happening in reality, but never the less, it is what everyone calls it. A SYE should probably be called a SYR (slip yoke relocator) or something like that.
If you look at your rear drive shaft, you will see that it is a solid piece of metal with a couple of u-joints and a female end at the transfer case end. At the transfer case, the drive shaft (female) slides over the transfer case output shaft (male) and creates what is termed a 'slip yoke'. As your rear axle moves up and down, it causes the drive shaft to slide in and out over the transfer case output shaft. What the SYE does is move the slip yoke from being at the transfer case and puts it in the drive shaft. A SYE will change the connection at the transfer case from a slip yoke to a U-joint. That means you will need a new drive shaft that has the slip yoke built into it (look at your front drive shaft to see one, since they used that on the front drive shafts).
The reason you may need a SYE is if you muck with the angle of the drive shaft too much it will cause the female part on the drive shaft to bind on the transfer case output shaft. You can muck with the angle of the drive shaft in a couple of ways: 1) you do a suspension lift which lifts the frame (to which the transfer case is ultimately attached) which causes the angle to change (some suspension lifts are not significant enough to cause a problem; some suspension lifts will come with spacers to drop the skid plate down which will reduce the drive shaft angle); 2) you do a tummy tuck which raises the transfer case and thus causes the angle to change.
Since a SYE needs a new drive shaft, this is another one of those things where you want to plan out all of your upgrades to make sure you are not going to have to buy another drive shaft when you make another upgrade and to make sure you have all of your money lined up...depending on your plan. Doing a SYE requires three things to be purchased: SYE kit (can be a hack-n-tap or a full SYE), a new drive shaft, and adjustable control arms. If you think you want a tummy tuck (LCOG ground clearance) and a suspension lift (larger tires), you probably want to do them at the time you do the SYE so you can get an accurate final measurement for the drive shaft. The guys at Tom Wood's made what seemed to me to be a big deal over getting an accurate measurement down to the nearest 1/8". I found it odd that a drive shaft with a 4" stroke would be at risk over 1/8" variance, but they were serious about me getting the measurement accurate. You may find that another shop will tell you that once you get their shaft you can do other modifications without having to have a new drive shaft.
Ok, definitely helpful. I knew that changing the angle of the drive shaft too much would require that I also change out the stock drive shaft to minimize the additional stress placed on it, and to help minimize the vibration. I didn't think the variance would matter that much, especially since there was that much stroke available.
As I will be going to 35" tires, doing a belly up, a suspension lift, upgrading at least the rear diff, I'll be sure to include the drive shaft in that as well. Do most aftermarket drive shafts come with an SYE? I wonder if the variance really matters down to an 1/8"?