When the pitrus (dead ancestors) come to the earth and have a look at their families. They want to know if the families are happy and that they still remember them. Many people perform shraddha on the death anniversaries of their ancestors. Even those people should perform shraddha during the Mahalaya Paksha.
Some people perform sharddha at holy places like Gaya, Benaras, etc. and stop performing the yearly shraddha. Even those people have to perform the shraddha during Mahalaya Paksha. Due to some or the other reason, some people may find that they have not been able to perform their ancestors’ shraddha in a particular year. These people have to perform the shraddha on the particular tithi of the ancestors’ death during Mahalaya Paksha. Others may perform the same shraddha during Sarvapitru Mahalaya Amavasya.
Pitru Paksha begins from the next day of poornima. People, whose ancestors have expired on a poornima, need to perform the shraddha on poornima. For these people, the Mahalaya Paksha begins from poornima.
On the sankashti after poornima, some communities bring a Ganesha idol for one day and consign it to water the next day. Often people bring as large Ganapathis as those brought during Ganeshotsav. This is called Tila Ganapathi. The offering of modak for this Ganapathi contains sesame seeds (black or white). During the offering of leaves to this Ganapathi, sesame leaves, sami leaves, etc. are used.
During these days, the charity of stuff liked by the pitrus of a family, should be given to poor people and qualified Brahmins. People may or may not perform poojas; these shraddhas need to be performed. That is the importance of Mahalaya Paksha. The reason I shared this post was that many newly married girls and others, who have separated out from joint families have called up Mom to ask her how to go about these rituals.