1what it is for
It lifts a single dirt block, turns it into a ball glued to your cursor, and lets you drag that ball anywhere on screen, straight through walls. Let go and it falls, keeping whatever momentum you gave it, then sets back into solid ground wherever it stops. Grass counts as dirt for this, including the corrupt, crimson and hallowed kinds.
the useful cases
Anything you want done at a distance. Pull the block a boulder trap is resting on and set it off from across the room. Wall yourself in when something is chasing you. Bridge a lava lake without standing over it, since the rod will place blocks inside lava where you could not. It also breaks Larvae, so you can start a Queen Bee fight from outside the hive rather than walking into the middle of it.
when to stop carrying it
Once the Mechanic shows up, wire and actuators do all of this more precisely and without dragging a cursor around. The rod keeps a niche in liquid plumbing, where opening and sealing one block at the bottom of a tank is quicker to build than a wired gate, but it stops being something you keep in the hotbar.