Knowing is about getting a good picture of the situation, gathering the evidence, logs and environment. Knowing is more than just the technical aspects of the situation. Registering the impact of the issue on the customer and consequences of the issue is as vital. That will be the driver for the pace of intervention.
Understanding is built buy pulling the knowledge from the gathered evidence and placing that along side a detailed insight to the environment in which the situation arose. The situation could be a PC failure, Data centre outage or a car that won't start. Unless there is good understanding, technical support is just Googling, "been there done that" and guess work. Lets not pretend a lot of tech support can be done with just a browser, research and good set of documents but moving beyond first line take understanding of product, environment and the interactions that bind them.
Predicting is vital to the technical support process and is more than just guess work. Based on a clear knowledge of the problem, an understanding of what changes can be done to vary the situation, prediction will provide the answer. Sometimes that prediction is based on hard logic and sometimes a combination of intuition and research but you can be sure that the techs that can effectively predict the outcome of their recommendations close more cases first time. Predicting, at it's best, is as near to science as tech support comes. A few experiments may be needed to set the direction but that last interaction along the lines of "This *will* solve your problem" is a thing of beauty. The "will" is emphasized because if you get a "could", "should", "might" the outcome is not certain.