To be in trouble.

1. When you are in a serious amount trouble.

e.g. "Im in deep shit."

2. A seriously dark or over thought idea.

e.g. Person 1: "Life is completely pointless"
Person 2: "Wow, thats some deep shit."

3. When you are in the middle of a shit and you start going into deep thought and all ignore around you, eventually realise you spend way too long on the toilet then you should have.

In a (very) bad situation

1. Listening to or looking at comments on Vsauce and being in that sort of trance of being mind-blown.

2. A very philosophical topic, talking about why the universe exists, why we are alive, what (if any) is the purpose to life, what kind of life (if any) is there in the universe, Etc.

"deep shit - n. the shit to end all shits; the best shit on God's green Earth"
Typically a shit in which you have expunged all the shit out of your anus in a deep grunt

see shitfuck definitions 2, 3, 4

to be deep in fecal matter