Ādi (Ashadha) between mid of July and August: The month of action towards victory
Sun’s annual transit over Cancer is called the month of Ādi (Ashadha) in the sidereal solar calendar. It usually falls in between the mid July and mid August. Sun’s direct aspect usually falls on the nakshatra of Uttarashadha on full moon of this month, hence the name. This is the time of informed actions towards victory over objectives. Uttara Ashadha is the nakshatra of later victory after strategic planning or contemplation over a long time. So this month will have the theme of achievements you’ve been thinking of lately. If you look at the previous month it was about finding and understanding the deeper meanings. Thus the following month automatically gives you the time to plan/organise your actions towards later success. It doesn't matter how big or small your achievement is, victory is victory.
This is the time of the year when Sun stops moving north and prepares to move south like it does every year. So from next month onwards the lands in the northern hemisphere will start having less and less daylight.
Religious and spiritual significance
Since the Sun’s movement towards the north is coming to a halt, this month is considered as setting Sun. Our one year is one day for the devas based on their dimension. This is their evening time, the time of setting Sun, the starting of tamassic time. So this month is spent in worshipping the dark Gods such as Rudras, Bhairavas, Das Mahavidyas, Ashta Matrikas, Navadurgas. Dark God doesn't mean what you learn from western mythology, Hindu philosophy says that when you are in the dark time aka tamassic time you need the blessings of dark Gods such as Kali to find the light. If you look carefully, Hindu philosophy says that even Lord Shiva is a dark God thus worshipping Shiva Lingam in black colour. He’s the representation of nothingness (no colour), but that nothingness leads you to everything like black hole creates galaxies.
Auspicious ceremonies such as marriages, inaugurations will not be conducted in this month due to the start of tamassic time. Some people also observe Ashadha navratri in this month annually to start the setting sun with prayers and poojas.
Ādi Kiruttigai (ஆடி கிருத்திகை)
Krittika nakshatra aka the Pleiades constellation is where Lord Kartikeya was raised. So worshipping Kartikeya on this day of this month is highly auspicious. People perform special pooja for their various prayers to get fulfilled. If Krittika is a war hero then Uttara Ashadha is where he fights. Thus the connection.
Overall, this is a good time to contemplate your thoughts, words and actions since past six months (from when sun was in Capricorn) to become the final victor.