БАБЬЕ ЛЕТО is a period of warm, sunny, and dry weather before the cold and rainy days of the fall. In the middle part of Russia, ба́бье ле́то usually starts in the middle of September and lasts several days. In English this spell of summer-like weather is known as “Indian summer”. The idiom ба́бье ле́то literally translates as “woman's summer”.
ба́ба - ба́бы – archaic noun for “woman-women”
ба́бий, ба́бья, ба́бье, ба́бьи – adjectives related to ба́ба