What is quantum physics?
Like other branches of physics, quantum physics seeks to explain basic properties of materials and physical objects. This includes descriptions of how they move (Newton's Laws), how energy is transferred, and things like this.
When looking very closely at the properties of atoms it was found that the traditional physical laws needed some modification to correctly explain observations on very tiny scales. It was found that the motion of electrons around atoms couldn't move with just any speed. Rather, the energy states are quantized into specific levels: 1, 2, 3, 4, etc.
Furthermore, the mathematics of quantum mechanics describes the ability of a particle to be in more than one quantum state at the same time. Some people refer to this as "quantum weirdness" - our ability to describe a quantum system is very different than they way we ordinary interact with the world. We can't always say what energy level a particular electron has. We can only describe the probability of that electron having energy 1 and the probability of it having energy 2.
When we try to scale these descriptions up to ordinary objects the inference is silly. We ask, how fast was the runner moving? We don't answer, "There is a 50% probability that he is moving 10 m/s and a 50% probability that he is moving 1 m/s." In the world of quantum mechanics, such statements actually make useful descriptions of the forces between atoms and why neon signs glow with particular colors. It's helpful in describing why water freezes and why ice is slippery. It was used in the design of the device you are using to read this message; everything from the computer chips to the display.