Structure in the Universe — galaxies, galaxy groups, clusters, and superclusters — forms from regions of the Universe which are denser than the average; dense enough the overcome the expansion of the Universe and collapse gravitationally.
Whereas it was previously thought that the largest structures collapsed first, later fragmenting to smaller structures (Eggen et al. 1962), we know now that structure has formed in a "bottom-up" manner, meaning that smaller structures form first, and progressively larger structures form subsequently.
The first structures to form were clumps with masses of roughly a million Solar masses (e.g. Mo et al. 2010), some 100 million years after the Big Bang. Galaxy formation peaked after 2–3 billion years, while most clusters of galaxies only formed several billion years later.
When a structure forms, it doesn't of course do so instantly; it takes some time to "withstand" the expansion of the Universe and collapse, for the matter to whirl around, settle down gravitationally, and reach a final, dynamical equilibrium. When this has happened, we say that the structure has virialized (from the virial theorem).
Today, clusters are the largest structures in the Universe to have virialized. As you write, the Milky Way is part of the Local Group, which is part of the Virgo Cluster. But substructures do move around, and although we are gravitationally bound, we're in fact currently moving away from the center of the Virgo Cluster (Arp 1988).
Superclusters are not yet virialized. They will be in the future (e.g. Araya-Melo et al. 2009), but due to the accelerated expansion of the Universe the galaxies will be so far apart that we might not be able to see most other galaxies (Nagamine & Loeb 2003).