Associational memory, as its name implies, is a type of memory that allows one to fuse multiple events in memory. If your boss constantly yells at you in his office, you might begin to form some bad memories of being in that office. While the phenomenon of associative memory is a familiar experience, the neural basis for it isn’t well understood. A prominent theory, which was formed in the mid-20th century but only tested recently is that neurons encode associations by wiring together. In the boss’s office example, the sight of the boss’s office might activate one subset of neurons, and those neurons would then “fill in” activation of neurons that code for fear or memories of yelling (obviously this is a gross oversimplification - I’m only using it to demonstrate the principle).
The neocortex is an evolutionarily new part of the brain unique to mammals and is responsible for high level sensation, movement and cognition. It wouldn't be fair to summarize in a sentence or two what cortex "does," but it is clear that it is an important part of the brain. Korbinian Brodmann famously divided the human cortex into about 50 areas based on histology of the six cortical layers in different parts of the brain; Brodmann's areas are still used today because their functions follow their histological structure. While cortical areas have largely stereotyped wiring patterns, some connectivity “motifs” are thought to be area-specific, varying based on the type of input the area receives. It is unknown whether the type of input (i.e. statistics of incoming activity that vary with types of sensory stimuli) to a given cortical area determines the types of connectivity motifs present in that region. And while classical cortical “rewiring”experiments from Mriganka Sur’s lab have shown that primary sensory cortices are somewhat tolerant to process foreign inputs, it is not clear to what extent those circuits constitute basic computational units or if foreign inputs cause reorganization of connections within the circuit.