I'm writing this letter to tell you about my new home的to在此的解

这里to并没有实际意义,只是引导后面的短语作为一个不定式来修饰letter,即一封告诉你关于我新家的情况的信.
不定式在句中一般强调目的,例如这句话,我给这封信的目的就是为了告诉你我新家的情况,如果你比较难受你可以把to翻译成是“为了”.例：
I want to go to school to learn some knowledge.
There are many ways to solve these problems.
You should read more textbooks to make your english better.
不难看出这些不定式一般接在名词后面.