I feel like everyone who has responded here has glossed over the fundamental definition, and is therefore missing the technical aspect of this discussion, which I would like to correct.
Veering and backing are
relative terms (not absolute):
-veering means "turning clockwise" (either with height or time)
-backing means "turning counterclockwise"
Saying "winds are backed" is technically ambiguous unless proper context accompanies the description, or unless everyone already agrees on the context without saying it. In the chasing world, this tends to be the latter, but for those who are new to the science, this is not at all clear, and one can end up misunderstanding the true concept underlying the jargon. Southeasterly winds are not, by definition, "backed", but they are backed
compared to southerly or southwesterly winds. Likewise, a westerly wind is not "veered" all by itself, but instead is veered
relative to a southwesterly or southerly wind, for example. Meteorologists use jargon like "backed" and "veered" winds as shorthand for saying "favorable flow for...(whatever...moisture return, adequate directional shear, slow storm speeds etc.)".
So in essence, the phrase "backed shear profile" is pretty meaningless without context. Same with "veered shear profile". Better terms to use would be "winds backing with height" or "veering wind profile". Outside of the context of the mid-latitudes of the northern hemisphere, the meanings that others have described above is much different, and may be perfectly backwards (in Argentina, for example).
I believe
@StephenHenry generally knows what he's talking about, but I disagree with some of the descriptions in his post. All hodographs he showed are effectively the same as far as their impact on existing convective storms (remove the axes and coordinate markings and you would be hard pressed to distinguish between them). As he correctly mentioned, winds veer with height in each profile and thus I would consider them all "veering wind profiles". But they all have about the same SRH, so the descriptions of "more streamwise vorticity" under the "backed" graphic is factually incorrect (especially without markings indicating the distribution of the shear in those hodographs; I presume the red means 0-3 km AGL, as is pretty common on many websites, but that is not some sort of official standard or anything; if the distribution of the shear in those profiles differed, then we could talk about differences in their impacts on storms, but based on the color distributions, they don't appear to differ). What differs between them is the location of the storm motion vector and how that would impact a chase strategy. A storm chaser would generally prefer "backed" low level winds because it would not only enhance SRH (assuming the mid- and upper-level flow does not also shift, which is
never a given), but would move the storm motion vector closer to the origin, thus implying slower storm speed, which is much easier to chase in a car from a road-relative perspective (which we humans are glued to, but storms are not).
The responses from others in this thread continues from here regarding the learning process and meaning of "backed" and "veered" as they pertain to forecasting severe storms.