Dynamite is most easily described as the poor man's grenade: it is thrown, after which, it explodes. It has a visible fuse on it, allowing the user to gauge when it will detonate. However, there is no 'safety device' on it, which means that it can explode in the user's hand, causing a solid amount of self-inflicted blast damage.
Dynamite is best used against slow enemies or vehicles, such as RHIBs. A good tactic for missions like Henbane River Gunboats is to find a bridge, wait for the RHIB to pass underneath it, then throw the stick of dynamite directly into the vessel. This can also be used to great effect against Bliss-carrying trucks, by throwing it on the road in front of the vehicle, especially if it is slowing to go around a corner.
With enough practice, Dynamite can be used against many other enemies. Idle Cultists can be quickly dispatched with dynamite, though it is not impossible that the enemies could notice the stick and escape the blast radius in time.