I guess they were intended to be more like some kind of 24th Century padded flak jackets, worn over the standard black jumpsuit (at the time with branch colored shoulder yoke and gray undershirts).
From a physics point of view it probably doesn't make sense but I guess you could argue that it's some sort of ablative armour that absorbs and dissipates hits from energy weapons...? I guess maybe it would be the usual trade-off between full protection and flexibility and manoeuvrability. Equally, perhaps there are practical reasons why personal scale energy shields (like those from Dune) wouldn't work in the Trek universe - or maybe it's the fact that passive protective clothing cannot be detected by scans but active systems like shielding give off an energy signature that can be picked up by an enemy...?
As to the design and appearance - it's really VERY simple and I strongly urge you not to over-think this one: these are costumes from a TV show and the production staff just wanted to keep something of the Starfleet "corporate look" for these additional uniform elements (like the branch colored stripes on the non-standard uniform variants used in Voyager at around the same time).
Let's face it, in a time of tricorders and long-range scanners camouflage and concealment (at least as we currently understand it) is a pretty redundant concept.