40d:Calendar

The dwarven calendar is used to display dates, and is visible in the upper right corner of the Overall Status screen (z). One year has 336 days and consists of twelve month in four seasons, with three months per season. Every month has 28 days. The months are named after kinds of stones, ore, gems and wood. New Year's Day and the first day of spring both fall on the 1st of Granite. New Year's Eve and the last day of winter both fall on the 28th of Obsidian.

The game's first playable year begins whenever the world stops generating, due to certain parameters you or the game has set up. By default, the world will stop genning when a percentage of megabeasts are dead, currently resulting in the starting years being in the low 200s to mid 300s on average.

Months and seasons

•	Granite	Early-	Spring
•	Slate	Mid-
•	Felsite	Late-
*	Hematite	Early-	Summer
*	Malachite	Mid-
*	Galena	Late-
•	Limestone	Early-	Autumn
•	Sandstone	Mid-
▬	Timber	Late-
♦	Moonstone	Early-	Winter
♦	Opal	Mid-
•	Obsidian	Late-

Ages

Ages are determined by the states of the world during world generation. Some of the known things that influence the ages are: number of megabeasts alive and dominant civilizations.

List of known 'Ages', explanation and their (possible) triggers, the italic are in-game descriptions:
-Age of Myth
-Age of Legends
-Age of Heroes
Those three are most common. Almost every world starts from Age of Myth, goes through Age of Legends and ends with Age of Heroes. Those three are influenced by percentage of alive megabeasts and semimegabeasts. After passing certain (unknown yet) % value, Age of Myth turns to Age of Legends, and Age of Legends turns into Age of Heroes.
Killing Megabeasts that visit you in Fortress Mode is known to trigger change of Age. When there are very few Megabeasts/Demons left, breaking into a very bad place can also trigger an Age change.
The Age of Myth was a time when living gods and mighty beasts still held sway.
The Age of Legends was a time when powers of the world were fading.
The Age of Heroes was a time when the last of the powers fought their final battles.

-Age of (Megabeast' name)
-Age of (Demon' name)
Occurs mostly in pocket worlds, where there's one Megabeast/Demon with relative large kill list.
The Age of Flarrgh was a time when the dragon Flarrgh was the only great power in the world.

-Age of (Megabeast/Demon) and (Megabeast/Demon), eg: "The Age of Titan and Dragon" or "The Age of Two Demons"
Same as above, but with two notable Megabeasts/Demons.

-Age of Three Powers
Even better than above, three notable Megabeasts/Demons.

-Age of (Race name), eg: "The Age of Dwarves"
One race becomes dominant in the world, or it's the only race left in the world.
The Age of Dwarves was a time when dwarves ruled the world.

-The Golden Age
Civilizations are expanding, and there are no wars and other things for them to worry about.
The Golden Age was a time when various civilized races peopled the world.

-Age of Fairy Tales
Toady One' quote from 2008 devlog:

"I finally saw a world arrive at the Age of Fairy Tales, which happens if mundane creatures (ie humans) make up at least 90% of the world's civilized population with the requirement that there are still a few fantasy creatures lurking around. In this case, it was a kobold cave that their scouts never found. I guess all of the fairy tales were about people having their crap stolen."

The Age of Fairy Tales was a time when fantastic creatures were few and far between, and some even doubted their existence.

-Age of Twilight
There are no wars and other worries, but civilizations are too weak to expand or are crumbling apart.
The Twilight Age was a time when fantastic creatures no longer lived in great numbers.

-Age of Civilization
Seems to be triggered when the world is mostly occupied by civilizations and there's no more fanciful creatures around.
The Age of Civilization was a time when fantastic creatures were but mere stories told by travelers.

-Age of Death
The Age of Death is a time when there are no civilizations left alive. It is respected in Dwarf Mode, so no invaders, merchants, immigrants.
The Age of Death was a time after civilization had crumbled completely.

-Age of Emptiness
The Age of Emptiness is a time when there are no civilized beings left alive. This is a game state that can be achieved in adventure mode, because everything can be killed in adventure mode. However, the Age of Emptiness is not respected in dwarf mode; things will be re-populated.
The Age of Emptiness was a time when no civilized peoples existed in the world.'

Information taken from this Bay12 forum thread
Information about Age of Death/Emptiness taken from this this research thread

Farming

With the changing seasons come different weather conditions, depending on your climate. A typical temperate mountainside fort will have snow in spring and winter, with warm summers and colourful autumns. The seasons correspond to growing seasons from the farm plot q menu, which dictate what can be grown when during the year. See the List of crops.

Trading

Each season bar winter brings the possibility of traders from one race or another.

The fussy hippie tree lovers elves arrive in Spring with wooden crafts and weapons, cages (often containing exotic animals), various fruits and berries, and rope reed cloth items.

Humans come in Summer with their wagon bursting with supplies, eager for junk stone craft goods.

Dwarves come in Autumn and their departure is a fortelling of the cold winter to come. Ensuring the dwarves depart with a good profit will bring the best chance of fresh cannon fodder new migrants in the year ahead.

A goblin caravan may arrive during winter if your civilization is at peace with the goblins.