A "spline" - or more correctly, a set of splines - is one of a series of squarish ridges found on a shaft or within a bore - and typically, a splined shaft mates with a splined bore (the splines on the shaft are referred to as "outside" splines, and those in the bore are "inside.")
Splines are used for power transmission where the phasing of the shaft and recieving bore are not critical, and where easy disassembly of the shaft is required for maintenance and repair.
In our sense, splines are found in the following places -
Front Axle - pinion and yoke
Side gears and axle shafts
Axle Shafts and hub units
Front Driveshaft - Centre of shaft, where the shaft is able to "telescope"
Transmission - Input Shaft and Torque Converter or Clutch
Output Shaft and Transfer Case Input
Transfer Case - Input Shaft and Transmission Output
Rear Output Shaft and driveline slip yoke
Front Output Shaft and Output Yoke
Rear Axle - Input Yoke and pinion gear
Side gears ahd axle shafts
There are splines to be found within the transfer case and transmissions (used to mate gears to mainshafts and countershafts,) but you probably won't be dealing with them for a while.
Why are they important? The ability of a shaft to handle power transmission without failing at the joint is a function of material selection, shaft cross-section, and spline count (which determines the actual size of the splines.) Splines typically fail by "shearing" - where they are literally torn off at the root.
Splines are usually called out by shaft outside diameter and spline count - the number of splines around the shaft. Splines are almost always spaced evenly, but some application have a "doubled" spline for indexing (like on steering boxes.) An example is "1.125-10", which means a shaft with an outside diameter of 1.125 inches and ten splines around the perimeter (typical for out manual transmission input shafts.)
When the size of the shaft is known, unknown (but standard for application) or assumed, you can simply talk about the spline count of the shaft proper. This is often seen with some axles - like the ChryCo 8.25" (late XJ) - which has, I believe, either 27-spline or 29-spline shafts. Also, the AW4 had two output shafts - 21- and 23-spline, as I recall.
Typically, the finer splined shafts (higher count) can handle more torque due to the increased area of the splines available to work against the shearing force. In some cases, a higher spline count can also indicate a slightly larger shaft - again, an advantage when handling large amounts of torque.
Does this make a little sense? I do tend to go on a bit...
5-90