The nine divine nights at the beginning of "Sarat" Rtu - ASvayuja mAsam Sukla paksha is the sarannavarAtri.
Rta (ఋత, ऋत) means the divine order, that which appears to change in a controlled manner within the satyam (సత్యం, सत्यं) which is unchanging reality. In the samvatsara (సంవత్సర, संवत्सर) a year in which the light and darkness, heat and cold, rain and shine all become equal proportions is satyam. Whereas the Rtu (ఋతు, ऋतु) vasanta, grIshma, varsha, sarat, hEmanta, SiSira appearntly change from pleasent spring, summer, rainy, pleasent sarat, autumn and finally cold winter signify birth, childhood, growth, youth, middle age, old age and death. So the body + mind + intellect is called as Rtumantam (ఋతుమంతం) that which changes thereby makes one enjoy the various aspects of the life's satyam.
After vasanta, grishma, varsha Rtus (chaitra, vaiSakha, jyesTha, AshADha, SrAvaNa, bhAdrapada months) starting Asvayuja month the SaradRtu will start which is half way mark in the samvatsara. So Sarat Rtu is equavalat of youth of the body where one should devote a good amount of time in worshipping godess of power i.e, Sakthi (శక్తి, शक्ति). It is symbolically represented as navarAtri in the middle of the year.
Sakti or dEvI worship conquer over the internal daemonic forces like madhu-kaiTabha (one drop of honey and several insects around it) that symbolizes the "I" and several "mine" (ahamkAra and mamakAra), sumbha-nisumbha i.e, kAma - krOdha and mahishAsura the animal nature called "lust"
So, mArkanDEya purANa - dEvI mahAtmyam states the importance of yearly sarat kAla pUja:
शरत्काले महापूजा क्रियते या च वार्षिकी ।
तस्यां ममैतान्महात्म्यं श्रुत्वा भक्ति समन्वितः ॥
So, what is the way one should carryout this puja. The best is (as per Siva purANa) :
శ్రోత్రేణ శ్రవణం తస్య వచసా కీర్తనం తథా
మనసా మననం తస్య మహాసాధనముచ్యతే
SrOtrENa SravaNam tasya vacasA kIrtanam tathaa
manasA mananaM tasya mahAsAdhanamucyatE
Hearing about his/her stories by ears, talking about his/her greatness by the voice
remembering his/her lIlAs by the mind is called the greatest sAdhana.
If this is not possible (to concentrate that way) it is possible to carryout nine different alankaaraas every day and worship the godess on all the nine days. That signifies only the alankaara changes but the underlying dEvI tattvam is always the TRUTH which is unchanging in nature.
Let the grace of godess durga dEvi be on one and all! Happy Sarad-navarAtri to one and all!!