Stress cones are usually not required on 2.4/4 kv power cables in conduit, but are required on higher voltages. Imagine concentric tubes of electrical field lines inside the cable, being confined by the outer semiconducting shield. The entire cable from the center conductor to the semicon jacket then is full of these tubes. When terminating the cable it is of course cut, then the semicon jacket is stripped back for a distance appropriate to the voltage. If the cable is then energized you can imagine the tubes of the electrical field in the vicinity of the end of the semicon jacket will simply curl back around extremely sharply, while those near the center will curl back around at a greater arc. The effect of this will be ultimate failure of the dielectric at the point where the semicon is terminated. What you would have in effect is say 7200 volts separated from the grounded semicon jacket by only 1/4 inch of dielectric. The solution to this is to install a "stress cone". If you can now imagine a metal cone, say about 3 to 4 inches in diameter by 6 inches long, with the pointed end cut off, inserted onto the cable, small end first, to the end of the semicon jacket. If the cable is now energized you can see that the tubes of the electrical field are curved in a much greater arc, so the electrical "stress is relieved". In practice there are several ways to do this. One is to use a manufactured "stress cone", which actually looks like a double ended cone. One end is semicon, the other is dielectric. The semicon is slid down so that it makes contact with the semicon jacket of the cable. A taped up stress cone can be made by using insulating tape to make about a 3+ inch diameter ball at the end of the semicon jacket, then applying semicon tape to form the cone. The semicon is made into a cone, and not allowed to curve back. There is one method that uses some sort of chemical to make a stress relief that looks like a sieve, but I don't understand how that works. The large porcelain potheads have stress relief built in.
I think BIL is Basic Insulation Level refers to the ultimate voltage at which some device will flashover. For example, an overhead primary distribution pole built for 12 kv will flashover at say, 60 kv. Not sure what the proper voltage is, but that's the concept.