interpret (something) as a sign

To "interpret" something is to guess or decide what it means. You "interpret" a person's actions, an unclear statement that someone made, or a symbol in a story:

I interpreted his silence as an admission of guilt.

How would you interpret this latest announcement by the Obama administration?

The thing that you're talking about comes right after "interpret". Then the meaning that you give to it comes after "as":

interpret a smile as a good sign

One of the most commonly-used words with "interpret ___ as" is the word "sign". A "sign" is like a symbol. It's one small detail which represents a larger meaning. Here are a few examples of signs:

• People sometimes think that God is giving them a sign. For example, if someone is living an immoral life and then gets into a car accident where they almost die, they might interpret the accident is a sign from God that they should be living a more serious life.
• People often look for signs of how the economy is changing. You can interpret good sales in one quarter as a sign that the economy is improving.

that

Use "that" to refer to something that a person just said:

A: I'm going to try to start a career as an actor.

B: So does that mean you're moving to L.A.?

Or you can talk about something that you heard on T.V. or radio using "that".

let (someone) go

There are two meanings for this phrase. One meaning is to allow a person, like a prisoner, to leave. The other meaning of "let someone go" is similar to letting an object go. It means to emotionally accept that something is gone. This is similar to "moving on".

This second meaning is the one that's used in the example above. You can imagine that, in the novel the speaker is talking about, the character did something like deleting his ex-girlfriend's phone number from his phone.