First, let me encourage you to answer this question personally for a dream you have actually had, and only use answers here as examples to help get you started.
I have recurring nightmares of tornadoes, which I hear is not actually uncommon. Sometimes the nightmare is the threat of a tornado which never hits (but I am waiting in fear of it coming at any moment) and other times the tornado is actively destroying things around me. Once, I was personally picked up and thrown by the tornado, but of course in the dream things seemed to happen in slow motion and I was not hurt.
If I was to analyze this dream according to Freud (one of the first and most common psychological dream analysts) I would seek within my dream to find an inner desire that I wish to be fulfilled. Even nightmares, according to Freud, have an element of wish-fulfillment. Perhaps destructive tornadoes then, represent my desire to gain a sense of control (be in as much control as the tornado seems to be), or maybe these dreams reveal an inner desire to destroy something that is causing me anxiety, fear, or panic in my life.
More modern dream analysts (like Ann Faraday), suggest the meaning of dreams most often have something to do with thoughts that have preoccupied the mind within the last day or two. To anyone who has dreamt of a major upcoming events (like a wedding, graduation, or surgery), this seems obvious. Faraday's analysis of tornado dreams makes the most sense to me because I only dream of tornadoes when I am particularly stressed out or anxious. According to Faraday's method of analysis, my tornado dreams directly reflect my anxiety and stress and could be an effort of my subconscious to relieve pent-up emotions that are the result of feeling out of control. Perhaps not ironically, I do not seem to be alone in dreaming of tornadoes (or other highly destructive acts of nature) when stressed.