Whayt are the colored swords that display over the top of the heads of the characters in the character screens inside their portraits? WHere is it in the manual if it is in the manual? AM I missing something? I have teh pdf manuals and I didnt see it.

From "manual addon.pdf" for Gallean's Return, page 2:

High-Level Unit Icons
When a unit achieves a certain number of levels over its base level, an icon will appear on its portrait to indicate its experience. A unit 5 levels above its base level will have a blue sword for an icon,
a unit 10 levels above its base level will have an orange sword for an icon, and a unit 15 or more
levels above its base unit will have a red sword for an icon.

In practice, these icons are a bit inconsistent, so don't rely on the exact level thresholds.

As said above. Blue is when the unit is 5+ levels above its base, Orange for 10+ levels and Red for 15+ levels.

It counts the levels that unit has gained after it can't evolve anymore on the given map. So a level 17 Berzerker will have a red sword, but a level 17 Overlord will have an orange one, because Overlord's base level is 5, so will only get a red sword at level 20. I think this is what StormLord meant by the "inconsistency", but it's not.

Basically, it serves as a quick info on how powerful a unit is. If you see a lot of red swords, you can expect very strong units.

The inconsistency is for units with base level 1 (e.g. leaders and neutrals). They get the blue/orange/red swords at level 5/10/15, not 6/11/16 as expected.