A QuBit is an element of a quantum circuit.
Like regular bits, a QuBit has two states, 0 or 1. Unlike regular bits, a QuBit can be in a superposition of these states.
Point 1: This gives us a terminology problem: What should be meant by "state" when talking about quantum systems. This is a problem only if classical terminology is stretched too far. Accept that new understandings are needed for quantum systems, and don't get stuck in terminology issues.
Point 2: An understanding of "superposition" is needed. That would be a long topic to discuss by itself, and is not discussed here.
A single QuBit system isn't very useful. Using an operator to put a single QuBit into a state which assigns equal probability to either state then examining the state of the QuBit gives you the same result as a fair coin toss.
Point 3: "Operator" is another specific technical term. Loosely speaking, in a single bit system, operators might be "1" (set to the 1 state), "0" (set to the 0 state), "1/2" (set to the 1 state superimposed with the 0 state, with equal probabilities). Operators are more interesting when talking about more than one QuBit.
In a quantum circuit which has multiple QuBits, the states of QuBits can be entangled with each other. The circuit is programmed by applying quantum operators to pairs of QuBits. This puts the entire circuit in an entangled state. At this point, meaningful computation becomes possible.
Point 4: "Entangled" gives us the last technical term. This is another long topic which is not discussed here.
That's a start. To understand how computation is done using QuBits, all of the above should be understood. That will require understanding a number of computer science concepts as well as a number of concepts from quantum physics.
Point 5: Wait! What about complex numbers and probability amplitudes? Or 'ket notation?
All of that is important when talking concretely about superposition, entanglement, and operators. But one step at a time. This answer is to provide a brief description of what is a QuBit.