From the very name, one can infer its significance. It is said that distribution of curd rice in this hot summer month is laudable. The significance of this month appears in the story of Bhageeratha. Shiva orders Bhageeratha thus:
"In Jyestha maasa, wake up early in the morning and having finished the daily rites, take a holy bath. Then pray to the Lord with the form of Trivikrama and distribute curd rice and water to brahmins. If you act thus for one month with devotion, thn Shri Hari shall be pleased and river Ganga, capable of washing away all our sins, shall descend to the Earth." Bhageeratha followed the orders, and the rest is history. It is to be noted that this month was instrumental in the descent of river Ganga. This description is available in the 'Bhavishya' puraana (भविष्य पुराण / ಭವಿಷ್ಯ ಪುರಾಣ).
ವಿಷ್ಣುರ್ವೈ ಸರ್ವದೇವಾನಾಂ ಜ್ಯೇಷ್ಠ ಶ್ರೇಷ್ಠಃ ಪ್ರಜಾಪತಿಃ |
ತಥಾಯಂ ಸರ್ವಮಾಸಾನಾಂ ಜ್ಯೇಷ್ಠ ಶ್ರೇಷ್ಠ ತಮಸ್ಮೃತಃ ||
विष्णुर्वै सर्ववेदानां ज्येष्ठः श्रेष्ठः प्रजापतिः ।
तथायं सर्वआसानां ज्येष्ठः श्रेष्ठः तमस्मृतः ॥
Meaning :- Just like Vishnu is the supreme among all Gods, so is the month of Jyestha among all other months.