What does the Reddening line represents in this U-B vs B-V plot?
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 $E(B-V)$.