According to the model currently in fashion, the cortex gets input into layer IV from sources including, among others, the corresponding 'core' part of the thalamus (cite White or Sherman) and other cortical areas (cite Van Essen 1985), and provides 'ascending' output to other cortical areas in layer III, or to 'other' parts of the thalamus and to motor efferents via layer V. There is also some thalamic input to layer I, supposedly from 'matrix' parts of the thalamus (cite Jones), but also as branches of the same neurons providing the layer IV input (cite Sherman).

In addition to the 'ascending' output mentioned above, however, there is a 'reciprocal' output signal to the same place (same general area of thalamus or cortex) that provided the input. This comes from layer 6 (cite Sherman) and possibly other places (cite Van Essen).

Let's assume that the traditional model is right about the semantic content of the input signal, e.g. the semantic content of a signal from a columns in V1 to antoher area (an output signal from V1's point of view, an input signal from the other area's point of view) is the presence or absence of a visual edge with a certain position and orientation, that the semantic content of higher visual areas is stuff like whether something is at a certain position and moving in a certain direction, or whether a certain object is recognized.

What is the content and function of the reciprocal signal?

First, an important question: does the reciprocal signal project to exactly the same 'functional unit' as the one that generated the input signal? For instance, in cortico-cortico connections between different cortical columns, if column A layer III projects to column B layer IV, then does column B layer VI always project to column A (possibly projecting to other places in addition to column A)?

Some possible functions: