It derives from its use in Frank Chadwick's campaign products for the original Command Decision, although the concept actually goes back to Arnold Hendrick's "1944".
When recreating a WWII operation, at that level of war, you can be stressed to portray entire divisions at even a reduced scale. So the number and size of units can be reduced by a rough factor of (usually) three, and then can be reduced by three or so again by the game scale.
So let's say you have a US armored division of three combat commands, comprising three tank battalions, three armored rifle battalions, and three armored artillery battaions, plus other supporting assets. You'd "bathtub" that organization to a single combat command, consisting of one tank battalion, a single armored rifle battalion, and a single armored artillery battalion. And then in Command Decision or a similar "platoon scale" game, each of those battalions would be reduced to a handful of vehicles, the lot of them standing in for a full armored division in the campaign.
In wargaming products with bathtubbed historical campaigns, such as Frank's "Bastogne" or S-2 Productions' "Operation Sealion", the organizations usually retain the names of the original, so that in the Battle of the Bulge, say, 28th Infantry Division would appear in the bathtubbed OOB as "28th Infantry Regiment".
Now, you're using Flames of War, which is notionally a 1:1 scale game. You could simply scale down divisions as brigades or regiments, or battalions as companies. Or you could step down the size two levels, to provide more variation in equipment types.
So, let's take the order of battle for 7th (British) Armoured Division in June 1940:
4th Armoured Brigade
- 7th Hussars
- 6th Royal Tank Regiment
7th Armoured Brigade
- 8th Hussars
- 1st Royal Tank Regiment
Support Group
- 4th Royal Horse Artillery
- 1st Kings Royal Rifle Corps
- 2nd Rifle Brigade
Divisional Troops
- 11th Hussars
- 3rd Regiment Royal Horse Artillery
You could "bathtub" it once, and have something like this as "7th Armoured Brigade":
4th Armoured Group
- Sqdn, 7th Hussars
- Coy, 6th Royal Tank Regiment
7th Armoured Group
- Sqdn, 8th Hussars
- Coy, 1st Royal Tank Regiment
Support Group
- Btry, 4th Royal Horse Artillery
- Coy, 1st Kings Royal Rifle Corps
- Coy, 2nd Rifle Brigade
Divisional Troops
- Sqdn, 11th Hussars
- Btry, 3rd Regiment Royal Horse Artillery
Then you'd have to mosh the task organization around a bit to give each player a bit of this and a bit of that.
Or you could "bathtub" it one level yet again, as "7th Armoured Battalion":
Sqdn, 7th Hussars (2 x plts)
+ Plt, 1st Kings Royal Rifle Corps
+ Plt, 4th Royal Horse Artillery
+ Plt, 11th Hussars
Coy, 1st Royal Tank Regiment (2 x plts)
+ Plt, 2d Rifle Brigade
+ Plt, 3d Royal Horse Artillery
thus creating a FoW force for one or two British players, representing all the regiments of the Desert Rats en petit.
Allen