Strip Brightness in a Spherical System
It is the luminosity in a straight strip like this:

(Credit: West 29 / CC BY-SA from here)
where the center of the strip passes a distance $x$ from the center of the circle at closest approach.  So starting from the center and moving out, each successive strip would have a progressively larger value of $x$, but $x$ is a constant for a given strip (with $x = 0$ for the center strip).
The only differences from the picture are that (a) the strips have an infinitesimal width $dx$, and (b) they are infinite in length rather than the finite circle shown here.