I'll briefly define some terms we may see frequently.
Channeling: This is an order the player frequently gives their dwarves. It directs a dwarf with the mining labor to dig a ramp downward through the earth (or other solid substance). The ramp connects the current layer with the one below it. Everyone and everything can walk up and down a ramp. Channeling a ramp is a good way to burrow down into the earth quickly, perhaps to use the earth as a shelter against wild animals or invaders, or to survey an aquifer.
Aquifer: Just like in the real world, an aquifer is an underground lake, and aquifers are found almost everywhere. In Dwarf Fortress, the dwarves can dig down through an aquifer, but the tunnel has to be constantly drained in some way and sealed, because otherwise the aquifer will leak forever (and “leak” is more like “flood”, here). An aquifer leaking out of control can drown miners who may be trying to seal it, and flood any living or working quarters beneath the aquifer. Aquifers usually occur below the first couple of layers of soil, and often lie above the rock layers.
Encased in ice: When water meets freezing air in Dwarf Fortress, it quickly freezes into a block of ice. If water meets freezing air and a dwarf in the same place, the dwarf is encased in ice. (And yes, the dwarf is now dead.) This can happen when a dwarf digs down into an aquifer in freezing outdoor weather, and then decides to stand right next to the unsealed (leaking) aquifer walls. There are plenty of ways to prevent this problem, but I didn't figure them out, in this case, until it was too late.
Tantrum: A dwarf who gets upset enough may throw a tantrum. Somewhat depending on his or her personality, a dwarf throwing a tantrum may attack other creatures at will, throw things, and break things. Sometimes after attacking, throwing, and/or breaking enough people/things, the dwarf will feel better and decide to stop throwing a tantrum. Sometimes the dwarf will just fall into insanity.
Insanity: There are several forms of insanity. In this case we saw melancholy. Tragically, the only cure for any form of insanity is death.