A quantum state is any of the various conditions that an object or system can be in, as described by quantum mechanics. A quantum state can be a superposition of different eigenstates, and it is usually represented by a ket vector.
In classical mechanics, an object or system has a definite position, momentum, and energy at any given time. However, in quantum mechanics, an object or system does not have a definite position, momentum, or energy until it is measured. This means that the outcome of any measurement on a quantum system is probabilistic.
The most famous example of this is the double-slit experiment. In this experiment, particles (such as electrons) are fired at a screen with two slits in it. If only one slit is open, then the particles will hit the screen at random locations depending on their initial momentum. However, if both slits are open, then the particles will interference with each other and create a pattern on the screen that cannot be explained by classical physics.
The reason for this is that each particle goes through both slits simultaneously and interferes with itself. The end result is that the probabilities of where each particle will hit the screen are affected by the presence of both slits. This phenomenon is called interference fringes.
Quantum states can also be entangled. This means that two or more particles can share a single quantum state even if they are separated by large distances. For example, two electrons could be spin-entangled such that they always have opposite spins no matter how far apart they are from each other. Entanglement occurs because all particles in the universe are connected through what Einstein called “spooky action at a distance”.