One should not trample and sit on the Gateway. What is the meaning for applying turmeric powder to that ( the Threshold) ?

All the Hindus  worship the Threshold as Goddess. Also think that Goddess Sri Mahalakshmi is in the form of the Threshold. So we do not trample it and also sit on that. Even if  the children do those two things without knowledge, the elders immediatley forbid them and make them know the reason.

In the evening twilight, Lord Sri Maha Vishnuh was in the incarnation of Sri Narasimha Swamy in Kruta Yuga, on this Threshold itself he    killed the might Demon Hiranya Kasipu  for the sake of this  World Peace. The boy, Prahlada  who was a great Devotee of Lord Sri Vishnu who was the son of Hiranya Kasipu. In the list of great Vaishnava Devootees, Prahlada comes first.

At the Threshold, the negative vibrations spread.

As this Threshold is symbol of Sri Mahalakshmi , that is adorned  with the turmeric powder and Kumkum  and worship that.

More over,in olden days in villages, snakes went  round every where and came into the house. So the people used to apply much turmeric powder to the Threshold (Gateway), with that strong odour of the turmeric the snakes and also other poison insects did not enter the house.