Models are great, useful things. Without being able to model systems, we wouldn't have many of the scientific discovies that give us current technology!
They simplify complex processes and can show us how we may be able to take advantage of a phenomenon to engineer new things. For example, the transister is a quantum mechanical marvel that powers more things than you'll likely ever realize. The microcontroler on your refrigerator, the amplifier on your stereo, and, of course, the computer, computer screen, keyboard, etc. that you're using to access this particular post! At its most basic level, the transistor is incredibly complicated involving all sorts of insane math, solid-state physics, and even a bit of chemistry. However, engineers use a simplified model of the transistor as a switch or linear multiplier. The transister, in terms of every situation is neither. However, over a certain range of circumstances it acts like those things! If we tried to keep the complicated physics characterization, engineers would never have gotten the research done to make many of our favorite devices! Imagine the difficulty in making a processor with millions of transistors if you had nothing to simplify the process. It wouldn't happen!
Now, whenever you simplify something, you remove some of its information. Inherently, this limits the effectiveness of the model, especially when pushed to its limits! For example, previous models of the atom always run up against problems of one sort or another. For example, atoms used to be thought of as "indivisible," and they certainly are the most basic unit of an element! However, that model was limited by not being able to explain the discovery of the electron. So, a new model emerged, where electrons were discrete units in a uniform positively-charged "pudding" (plum-pudding model). However, this new model could not explain experiments that suggested a dense central nucleus instead of a jello-ish mass. Thus, we got the Rutherford model, with a nucleus and electrons in orbit. Again, this model could not explain another detail! Niels Bohr went ahead and found out that electrons couldn't just have *any* orbit, but that hey were locked in discrete energy levels, so Bohr's model became a big deal. But then Bohr's model started to disagree with experiment and it could not explain many other things, like how chemicals bonded or how particles also have a wave-like characteristic. So, we come to our final (ambiguous) model, the electron cloud model. This model has been refined over time, but this seems like a good illustrative end point.
The list really could go further and further with models and their limitations, but they usually have one common factor. They help simplify a complex thing, but in doing so, they always leave something out. Whether or not that "something" is important depends on the situation, but that "something" is what limits our model.
I hope that helps!