I see this happen quite often. The vault tec boy pops up in the lower right hand corner holding 3 big wooden boxes, I don't notice what happens when he comes. Why does he show up? Does it mean anything?

your inventory is almost full... either sell stuff, equip stuff, or build more storage buildings.

It means you are going out of enough storage-room.

You can:

1. Sell some things to have more storage in your already built storage-rooms

or

2. Build more Storage-rooms to have more items in your Inventar.

Heh...

Rougefire was a little bit more faster

But i think you will get the point

I also had this happen when my vault storage was not even half full though. Like, when it was 30/80 or something. Maybe it's also related to having dwellers returning which would flood your inventory, in which case that should be removed, it's annoying.

I think it also appears when your lab or medbay produces another batch of radaways or stimpacks which exceed the maximum capacity.

Yes.

It means that your items storage is full, or your Stimpak storage is full, or your RadAway storage is full.

{Edit}

It should also be noted that adding Storage Rooms or upgrading existing Storage Rooms increase only item storage capacity. They do not increase RadAway or Stimpak storage.

Adding Medbays will increase your Stimpak storage You don't have to have Dwellers in them for storage, you only need them for production). Upgrading Medbays will NOT increase storage. I don't know if this is a bug or intentional.

Adding Science Labs will increase your RadAway storage. Again, you don't need to have Dwellers in them for storage, they are only needed for production. Like Medbays, upgrading Science Labs will NOT increase storage.