1An adverb meaning 'gradually, little by little, step by step.' Describes a change that progresses incrementally — in either direction (better/worse, more/less, hotter/colder). One of the most common adverbs in daily Japanese; in modern writing it's almost always spelled in kana だんだん, while the kanji form 段々 is more associated with the noun sense (stepped structures).
十一月に入って、だんだん寒くなってきた。
Now that November is here, it's been getting colder little by little.
毎日少しずつ練習していれば、だんだん話せるようになりますよ。
If you practice a little every day, you'll gradually be able to speak it.
日が暮れてきて、街の人通りもだんだん少なくなった。
As the sun set, the number of people on the streets gradually thinned out.
子供がだんだん大きくなって、今ではもう父親の背を抜いた。
The kids have been growing little by little, and by now they've outgrown their dad.
2A noun referring to stepped or tiered structures. Standalone 段々 for 'stairs/steps' is somewhat literary; in everyday Japanese it's far more often encountered inside compounds such as 段々畑 (terraced fields) or 段々の屋根 (tiered roof).
山の斜面いっぱいに広がる段々畑が、夕日に照らされて美しかった。
The terraced fields spreading across the mountainside were beautiful, lit up by the sunset.
古い神社の前には、苔むした段々がゆるやかに続いていた。
In front of the old shrine, a series of moss-covered steps stretched gently upward.