Retrain soldiers?

I'm guessing that it's referring to the fact that you can give new equipment to existing soldiers, either by trading it to them or by purchasing some from the merchants in your friendly towns.

The latter. Also, you can buy those items in the shop and equip them on your sovereign and heroes.

Yes I have my heroes geared up, but there is no way that I can tell of trading items to your non-hero units. They dont appear in either the shop screen or on the trade screen. Cycling back and forth between units just goes through my heroes.

There really should be a way (tech, building, etc.) that allows units (non champions) to upgrade!

I can trade items to my non-hero units.  Click their portrait circle so they are selected, and then click the "Trade Items" action in the tab to the left.

The problem I am having is that although my non-hero unit can carry the items I trade to them, they cannot use them.  That is, it appears that once I have trained a soldier unit, for example, they are stuck with the equipment they had when trained.  I also cannot unequip their items as I can with hero units.  I guess this makes sense in that if I trained a peasant with a club, he can't use a sword later.  All he knows is how to wield the club.

So the non-hero units can carry items back and forth to give them to heroes or your sovereign in the field, but they can only use the weapons and armor they had when trained.

I've only played the campaign, though, so I've not got the best experience with the game.  Maybe the campaign is restricting options for its gameplay purposes.

Maybe there is a tech later that will cause updates to go out to all your military units immediately.  I saw a loading screen tip that indicated that's the way it works with building upgrades like huts to houses.

"I guess this makes sense in that if I trained a peasant with a club, he can't use a sword later.  All he knows is how to wield the club."

Right, but the game mentions retraining, so hence I was wondering if there is a way of doing that or if thats just for designing new units.

I had the same question. Maybe I missing it but there doesn't seem to be a way to upgrade or retrain units.

The "upgrade" option basically just designs a new unit and leaves the existing one as is.

I think Kryo here was referring to the OP's two choices, and so yes, this means that when the game refers to "retraining" it means you can train NEW units with upgraded equipment, and not that the old ones will be altered from what they were when originally trained.