Co-conscious is a term used by multiples (people with Multiple Personality Disorder, Dissociative Identity Disorder, or empowered multiples) to describe the state of being when two or more people in the system are conscious of the events going on outside the body, or are aware of each other's thoughts. When a whole system is described as co-conscious, it usually means that everyone, or nearly everyone, is always aware of what is going on outside. This means that no one loses time. It also usually means that the people in the system can converse freely, and have access to each other's thoughts.
Being co-conscious with someone can be like sharing a telepathic link, and sometimes it is strong while sometimes weak. Two people who are co-conscious might only be able to share thoughts with effort, or they might have access to each other's memories only very foggily. Conversely, they might share all thoughts, feelings, and memories.
Most systems have a combination of co-consciousness and lost time, with a few multiple systems being at one extreme or another. Sybil, the famous multiple from the 60s, had almost no co-consciousness, and never remembered events from when her alters were out. It is more common to have a completely co-conscious system than one with no co-consciousness.
In therapy, being co-conscious is usually a goal. Some systems work on becoming co-conscious so they can integrate, and some systems see co-consciousness as a final goal, not wishing to integrate into one person.