A kigo is a word or phrase used in Japanese poetry that evokes a particular season. They are one of the three defining qualities of the classic Japanese Haiku. (The other two being a sense of juxtaposition and the 5-7-5 structure that is all most Anglophones know about them.) Shallow Parody of haiku (or Japanese poetry as a whole) overwhelmingly uses cherry blossoms in this role. We'll leave it to The Other Wiki to tell us about the significance of cherry blossomsnote (sakura) to Japanese culture, because the point here is that they only appear in spring. Mentioning them is a economical way of setting the season, and haiku is all about economy of expression.
Other common kigo are:
Spring: Warm (atatakashi or nurumu), the warming weather; uguisu, Japanese bush warbler, regarded as a harbinger of spring; Frogs: especially their calling
Summer: Hot/heat; Rainy season starting in mid-June; Wisteria which blooms in early summer and lotus in late summer.
Autumn (Fall): Coloured leaves; Typhoon, typhoon season is roughly June-December; Insects, implying singing insects such as crickets.
Winter: Snow, Cold, fugu soup, a seasonal dish, Christmas (modern).