Why are scientific models useful?
To help understand and predict the way things work.
All natural science is based on models.
Models are suggested and tested by observations.
If observations seem to confirm that the model is accurate, then the model can be used to make predictions pointing in the direction of more uses.
For example, models of fluid dynamics can be used to help predict how weather systems will move and develop.
Models of chemical reactions can be used to predict the results of using different reagents, etc.
Models of motion of masses under the influence of gravity allow us to plan and execute complex trajectories for space probes.
Beyond their explicit use in science, note that our brains interpolate and extrapolate all kinds of information based on models, allowing us to perform tasks like making sense of what we see, catching thrown objects, balancing, reaching out for objects in the dark based on our recollection of where they were, and many others. Much of our experience and ability to cope with the world is based on these kind of models.
One major thing to note about models is that they are not reality. Natural science is incapable of telling us what is actually true. It can only say that models seem to be good or not according to how well they fit observations. That is not to say that once a model is superceded by a more accurate one then it is no longer useful. For example, Newton mechanics is very useful, despite being known not to be 'true' in the sense that it is inaccurate at high velocities or very small scales.