While your explanation does touch on some of the key points, it misses our a few crucial details. Schrodinger's Cat is one of the most frequently quoted (and misquoted) concepts in quantum mechanics but you miss a lot of the subtlety in the thought process if you miss out details.
Picture the scene: you're a physicist in the early 20th century. You've spent your life studying what we would call "classical physics", encompassing newtonian physics, electromagnetism, fluid mechanics and so on. Classical physics like this is built on rules. You can use equations and models to predict how a particle or body is going to behave under certain conditions. You can predict the exact times of lunar and solar eclipses. You can create a battery and, from what you know about the acid concentration and metal used in it, you can predict how long it will light a bulb for. You can fire an artillery shell and accurately predict where it's going to land, at what speed and after how many seconds.
You (quite justifiably) assume that the same will be true for tiny particles. But the more you experiment with them, the more you discover that this isn't true. Instead of following discrete rules, these particles do lots of crazy things - they exist as particles and waves, or they appear to decide on what they do in some cases based off probability. You would do an experiment where, say, you fire an electron at a step potential (which would normally repel it according to classical physics) and occasionally there was a chance that it would tunnel through it. You discover that radioactive decay follows a probabilistic model whereby an atom has a probability of decaying within a given time period. And -most absurd of all - sometimes it was shown that particles could exist in a number of states, and you wouldn't know which state it was in until observed.
Schrodinger's Cat was a thought experiment to illustrate the bizarreness of this phenomenon. He hoped to give an example of a case where the probabilistic nature of quantum mechanics had relatable real-life effects. In the thought experiment, we have a radioactive atom which has a known probability of decaying within a given time period. We put it in a box with a detector which, if it detects a decay, breaks a glass vial of poison. In the box we also have a cat. If the atom decays within the time period then the vial is broken and the cat dies.
In a very isolated system, the atom in question is said to be in a "quantum superposition" of two states - decayed and not decayed. However because the fate of the cat depends on this state, it follows that the cat is also in a superposition of states - dead and not dead. And until the box is opened it is impossible to infer which state it is in. Obviously this flies in the face of reason, and that was the point - Schrodinger was illustrating that quantum mechanics had implications that went beyond the nano-scale.
And in fact, it wasn't until the theory of Quantum Decoherence was developed in the 90's that physicists finally worked out a solution to this problem, and showed why quantum superposition was only observed for simple, isolated particles (and not with cats).