Upvote:-1
Since the variation of the weather during the year has a regular component depending on position of the Sun with respect to the ecliptic, one has to define seasons with respect to this position. Knowing the seasons is important for agriculture, and there is little doubt that originally calendar was invented for the needs of agriculture. This was long before the invention of writing.
There are 4 conspicuous points on the Sun path: the 2 equinoxes (when the sun's path crosses the ecliptic) and 2 solstices (when the Sun is most remote from the ecliptic). The days when these events occur is not difficult to determine by direct observation.
They define the boundaries of the 4 (astronomical) seasons, and one of them (which can be chosen arbitrarily among these 4) is natural to define as the beginning of the year.
Upvote:-1
After some more research:
Astronomy has needed a strict definition of seasons at least since Callippus found that they were of different lengths (around 330 BC https://en.wikipedia.org/wiki/Callippus), as described in Ptolemy's Almagest. (Also indicating that equinoxes and/or solstice weren't precisely known long before that.)
That seems to have co-existed with other definitions outside of astronomy.
For the name it may be influenced by the similar ones: 'astronomical year' (introduced in 1740 by Jacques Cassini) and 'astronomical day' (introduced in the British Navy in 1767, http://www.royalobservatorygreenwich.org/articles.php?article=1087 ).