xenolithic breccia - As the authors note, this is the name given by Binns (1967) to a type of ordinary chondrite breccia that contains clasts of differing metamorphic grade or chondrite classes. Most of these types of breccia contain variations in metamorphic grade only and are also known as genomict breccias.
Wood (metallographic cooling) method - This method to determine cooling rates in isolated metal grains in chondrites was developed by Wood (1967) and is the basis for many of the authors' conclusions. With this method, the central Ni content in taenite grains is measured along with the distance to the nearest grain boundary (essentially the radius of the grain), and compared to what one would expect for various model cooling rates on a plot of Ni (y-axis) vs. distance to grain edge (x-axis) on what I'll call a "Wood plot" (e.g., Figs. 2, 4, 6, and 9 in the paper).
The method assumes that taenite was trying to reach Ni equilibrium according to the Fe-Ni subsolidus phase diagram (reproduced here). According to the latter, Ni content in taenite must increase as temperature decreases. However, because of finite diffusion rates in taenite, the actual Ni content will be lower than the equilibrium value. Let's see if we can understand why the curves on the Wood plots look like they do.
If diffusion in taenite is rate-limiting, larger grains will have lower central Ni contents than smaller grains for a given cooling rate, because Ni has further to diffuse in its attempt to reach an equilibrium value. This accounts for the negative slope of the cooling lines plotted in the Wood plot.
For a given grain size, faster cooling will result in
lower central Ni contents, because diffusion cannot keep up with the cooling
rate. Thus, on a Wood plot, various cooling rates are shown, with
higher cooling rates corresponding to lower Ni contents at a given distance
from grain edge.
polycrystalline kamacite - The polycrystalline kamacite noted by the authors is interpreted to have been produced by impact-induced recrystallization.
taenite types and textures - Various types
of Ni-rich metal are described by the authors. With decreasing bulk
Ni content these are tetrataenite, cloudy taenite, and plessite.
Tetrataenite (also called "clear taenite" because of its appearance
after etching in acid) is a separate mineral that can form upon slow cooling.
Cloudy taenite (because it appears dark & cloudy upon etching)
is a Ni-rich taenite (actually an ultrafine mixture of taenite + tetrataenite)
that tends to occur in the outer portions of smaller taenite grains or
the cores of smaller ones. Plessite tends to occur in the
centers of larger grains and is a fine-grained mixture of kamacite and
high-Ni metal alloy phases. The authors also mention "featureless
taenite", which lacks cloudy or plessite textures, and "zoned taenite",
which corresponds to any zoned taenite such as cloudy or non-cloudy taenite.
The main thing you need to know is that the authors applied the Wood method
mainly to grains of a particular type, those with cloudy taenite and rims
of tetrataenite, which they supposed are amenable to analysis with the
Wood method.