Simply put, we are dealing with frozen copies of events happening somewhere in time and space. One carries around these extra copies because one failed to handle something about the actual event. Once the unfinished business is completed, the extra copy is no longer needed and it will as such vanish -- it is "cleared".
We usually refer to the extra copies as "Incidents". That is somewhat confusing in that "Incident" could also refer to the event itself. However, by convention we would use the word mainly about a carbon copy of some event. When the extra copy has been neutralized, we would say that the incident has been "cleared" or "erased", or that it is "gone". The real event is still what it is of course, but it is the copy that will be gone. We could say that the real event is then more "clear".
The reason we might wish to clear these facsimiles is that they tend to mess up one's mental and emotional responses. Because, as opposed to the real events, the facsimile incidents get carried forward in the present. They become filters through which one is perceiving present time, and they become programs governing one's responses. That is often not very useful. Generally speaking one is better off actually dealing with what is going on now.
In the Re-Experiencing technique we locate incidents that are attached to unwanted reactions. We experience what is in them that hasn't previously been fully experienced. We go over the contents until the incident drops out of the present environment and regains its proper location. If we repeat that activity as many times as necessary we can transform unwanted reactions into more useful responses.