Emotional detachment is feeling as though you have no emotions, positive or negative. Generally, there is still somewhat of a negative/sad emotion present, but otherwise, emotions are not felt very strongly. In this state, it can be hard to even imagine happiness.
In the first meaning, it refers to an "inability to connect" with others emotionally, as well as a means of dealing with anxiety by preventing certain situations that trigger it; it is often described as "emotional numbing" or dissociation, depersonalization or in its chronic form depersonalization disorder.
When anxiety and depression hits you like a hurricane, you have tunnel vision. You can't see anything, but what's happening in front of you. You can't think straight, and you can't process what's going on or why this is happening. Then all of a sudden you're stuck, and you get sent away to recover from the battle you've been fighting for so long.