The word Mahalaya can be defined as Maha + Alaya, which means great habitat. The earth turns to a great habitat for these fifteen days; because the manes are invited from the upper space to the human habitat to be worshiped. During these fifteen days every family is expected to offer Tarpan (offering water) to the pitru as a token of obligation. Also any day within the fortnight according to suitability of the family, is fixed to offer Shraddha (ceremonial offering of food) for the pitru. (Symbolism of Mahalaya when it is considered as a day for making offerings to dead ancestors.) – Source - Unknown
Mahalaya means ‘the great dissolution.’ It stands for the dissolution of the ignorance within us which is symbolized by the killing of the Buffalo
If the Tapasya is proper, the ignorance within us should be wiped out in nine days. The buffalo is the symbol of Tamas and Inertia. It is the vehicle of Yamraj, the Lord of Kala – the great leveler of time. Kala slowly yet surely moves forward on the buffalo. So if we kill the buffalo in us, it means we go beyond the concept of time, which is the ultimate goal of wisdom – the going beyond limitations, the Liberation. (Symbolism of Mahalaya when it is considered as a day when Goddess Durga is invoked.) – R.S. Nathan