The particular quantum fluctuations that you seem to be referencing here are the fluctuations that occurred during inflation which led to the pattern of large scale structure across our observable universe.
In most models, inflation is driven by a single scalar field. Scalar fields are fields which can be described by a single number at every point in space. The specific scalar field used to explain inflation would have had to experience some form of potential energy, and inflation occurs as the field slowly moves from a higher-energy state to the minimum energy state (inflation ends when it hits the minimum energy state).
However, quantum mechanics guarantees that the final picture won't be quite this simple, because the field value is guaranteed to bounce around a little bit even though the overall motion is downhill (towards the potential energy minimum). This leads to some regions in the early universe having ever so slightly higher energy density than other regions. Those higher-density regions eventually become dense regions of the universe, such as galaxy clusters, while the lower-density regions become voids.
Cosmic structure is a consequence of the amplification of primordial density fluctuations due to gravitational instability. Density fluctuations can be represented by a power spectrum and plotted as a function of distance, or z, according to taste. The expansion rate of the universe fluxctuated initially and continued to do so until some time after matter energy equality was achieved [i.e., after onset of the matter dominated epoch]