A quantum state is exactly as it sounds. It is the state in which a system is prepared. For example, one could say they have a system of particles and at time, t=(some number)
…, the particles are at position qi (qi is a generalized coordinate) and have a momentum, p=(some number). You then know the state of the system. There are other properties that can be know for a particle. You could create a system of particles with a particular angular momentum or spin, etcetera. - A quantum fluctuation arises from Heisenberg's uncertainty principle which is \\delta E times \\delta t is greater than or equal to \\hbar and it is defined as the temporary change in the amount of energy in a point of space. This temporary change of energy only happens on a small time scale and leads to a break in energy conservation which then leads to the creation of what are called virtual particles. (MORE) 
