Strictly speaking, dynamite is nitroglycerin-soaked charcoal, pressed into sticks. A dynamite package is a collection of a few sticks, taped together, and wired in parallel to a simple timer. This timer can be set for as little as ten seconds of delay, or up to a few minutes. Dynamite is especially helpful for clearing cave-ins, and can blow most doors apart.
It is a relatively common sight in the wasteland, found in military installations and mines. Many storekeepers will also carry dynamite. Its use in combat is negligible, given that it can't be thrown, but it's useful to have to knock down lower grade doors (or improvise satchel charges to kill characters with). Note that the dynamite will be described as having detonated prematurely if it doesn't damage anyone (or the player character). However, even with the lowest possible Traps skill, it's extremely unlikely to suffer an incident.
It has one unique use: In the radscorpion cave, the player can use it to collapse the wall near the entrance, burying the scorpions within. The dynamite has to be dropped on the ground, activated, next to a wall section described as weak.