So you know how sometimes you go to someone else's house and they have different things and customs than you do at your house? It's kinda like that, but with countries!
A long, long time ago, people from India (which is a big country on the other side of the world) traveled to Southeast Asia (which is a bunch of countries nearby) to trade and explore. They brought with them their culture, ideas, and religion.
Some people in Southeast Asia liked these things that the Indians brought, so they started using them in their own countries. Things like Indian writing, religion, and traditions became popular in Southeast Asia over time.
This process of Southeast Asia adopting Indian culture is called "Indianization." It's like Southeast Asia was seeing what the Indians had and going "Hey, that's really cool!" and then taking those ideas and customs and making them their own.
So, the Indianization of Southeast Asia means that Southeast Asia became more like India in some ways because of the influence of Indian people and their ideas.