Deep soul searching is not an official psychological term. People use it informally to describe diving deeply into their inner world to explore emotions, beliefs, and experiences that usually sit below everyday awareness.
In practice it points to intense introspection: looking at old memories and patterns, noticing fears or limiting beliefs, and clarifying what truly matters. The aim is often to understand, release, or integrate what you find and to feel more meaning or connection.
Some also use the word in psychedelic or therapeutic settings for an inward journey where attention is turned fully inside, sometimes with eyeshades and music. Reports range from personal insights to spiritual themes, and experiences differ from person to person.
In short, it is a metaphor for deep inner work and, for some, exploring beyond the usual sense of self to better understand life. For a brief overview, see this explanation of deep soul searching. Hope this helps.