Irumudi Kattu means two packages. The front pouch is meant for Lord Iyappan, this pouch contains the ghee coconut (Nei thengai) and all the pooja items needed when we reach Sabari mala. The back pouch carries all the items we will need on the way for ourself. The front pouch cannot be opened until we reach sabarimala, the back pouch can be opened on the way. The most important item carried in the irumudi kattu is the ghee coconut (Nei thengai). The ghee coconut symbolizes the devotee himself who is carrying the irumudi.
It is said the coconut represents one’s body and the ghee represents ones soul. You carry yourself to be offered to Iyappan and carry back what is gives back to you. That is the reason you offer the ghee for Iyappan Abishekam and put the empty coconut in the burning fire. You can carry your ghee coconut and also of others from your family. They have to fill the coconut during the Irumudi kattu.
There is also another reason why people carry ghee in a coconut. It is said ghee is taken to offer to Iyappan and to keep it from spoiling we seal it in Coconut. These are the two meanings I have come across.