Computer models help us simulate a real life situation or process with some built-in assumptions (that is, the model is a simplification and works under certain assumptions). A model will help us study the effect of changes in some of the variables, without carrying out changes in the actual physical environment. For example, we can study how weather patterns may change with slight changes in wind velocity using weather models, instead of actually doing measuring variations out there in the environment. This results in substantial savings in material and resource costs.
Models can also be used to study complex and potentially dangerous systems, such as climate change modeling or nuclear testing. Computer simulations are also much faster, depending on the processing power of computer, as compared to physical models.
On the flip side, the models are simplifications of the reality. There are a number of systems we do not know much about, and hence computer models become oversimplified for such systems and cannot effectively replicate those systems.
Great processing power is needed for studying very complex systems. Some of the systems are way too difficult to model, simply because of the dynamic nature of such systems. For example, it is extremely difficult to model behavior of bacteria, for example, to study their movement through sub-surface, hence they only be studied through physical models and laboratory work. Any computer model would be unable to capture much of their dynamism.
Hope this helps.