Literally Akalbodhon is a bengali word, which is formed by combining two different words akal and bodhan

Akal means untimed or out of season
Bodhon means worship.

Conventional Durga puja is celebrated during Spring Time. Akalbodhon refers to the worshiping of Maa Durga during Autumn. This autumnal ritual is different from the conventional Durga Puja, which is usually celebrated in the springtime and thus the name Akalbodhon. Akalbodhon is not just a word it is much more than that. If you ask a Bengali "What is Akalbodhon" The answer you come to know is "Durga Puja". Durga Puja is not only worshiping Goddess Durga, it is a Festival of joy social gathering, good food and gift. By any means Durga puja is the biggest festival for Bengali communities.
Mythology of Akalbodhon
According to mythology thus goes the story of Lord Rama, who first worshipped the 'Mahishasura Mardini' or the killer of Mahishasura during Autumn before going on war with "Ravana" After this timing of the year to celebrate Durga puja become very popular.