What does the Reddening line represents in this U-B vs B-V plot? The plot is from this paper (pg-8). 
They have also talked(in the same paper) about how central stars from galactic longitude range $20^\circ-80^\circ$ will have a very unusual Reddening line (pg-9). The current plot is for central stars from the galactic longitude range $200^\circ-300^\circ$

The group
of planetary nuclei plotted here are all those occurring in galactic longitudes 200o
-300°.
In the longitude range from 20° to 80° the points fall to the right of the reddening line in
Figure 3 (not plotted). If the latter energy-curves are well-behaved, a very unusual
reddening line would be needed to explain their position in the diagram. This is a puzzling result which is unexplained at present.

My interpretation of Reddening line: It is showing that if we plot real star data where the sample contains all the stars from bluer end to redder end on this U-B vs B-V plot, we will get  the Reddening
line on the plot.
Is this interpretation correct?
The reddening line is the locus that a star would move along in a colour-colour diagram as the interstellar reddening towards it increases.
i.e. It is an equation on the colour-colour plot of the form (for this colour-colour plot)
$$E(U-B) = f(E(B-V)) + c\ ,$$
where $E(U-B)$ is the colour excess in $U-B$ due to interstellar reddening, $E(B-V)$ is the colour excess in $B-V$ and $c$ is a constant chosen so that the locus would go through a star of the same spectral type but with no interstellar reddening.
Typically, for low reddening and a typical interstellar medium
$$ E(U-B) = 0.72 E(B-V) + 0.05 (E(B-V))^2\ ,$$
which I imagine is the line drawn on the plot you show.
To establish the reddening to a particular star you can follow it back from its observed position in the colour-colour plot, along a reddening line, until it intersects the main sequence locus (if it is a main sequence star). The intersection would give its unreddened, intrinsic colours and the x-axis increment through which you traced it back would give its $E(B-V)$.