This house reminds me of the one I lived in when I was a child.

本意的表达应该是：This house reminds me of the house I lived in when I was a child.但是由于之前已经说的是house 了，所以就用one指代；
再给你个例句：this pen likes the one I gave you very much.这个钢笔很像我给你的那个。
希望能帮到你！

the one 指 house

这间房屋让我回忆起我以前住的房屋

the one =the house
one指代同类事物。

the one 指的是我孩童时期住的屋子

This house reminds me of the one I lived in when I was a child.
这间屋子让我想起了我孩童时期住的屋子

例句

The mountain reminds me of the one i climbed when i was a child.