What is "stacked unit needs an order" referring to?

I know that in Civilization 5 there is no stacking of units. However, sometimes when a unit needs an order, the blue button in the bottom right of the screen will say "stacked unit needs order" instead of what it usually says which is "unit needs order." If there is no stacking of units, what is this referring to?

Unit stacking is allowed in Civilization, its just restricted.

"in Civilization 5 there is no stacking of units" is an oversimplification. From the Manual:

Units are subject to “Stacking” limitations – two military units may not end their turn in the same hex, nor can two non-military units, but one military and one non-military unit may end their turn stacked in the same hex.

Because of this, there are two cases in which units can become stacked:

1. One combat unit can be stacked with one non-combat (civilian) unit by normal movement or other means like below. (And they may end the turn this way.) This means your worker is allowed in the same square as your warrior, which is important for defending your vulnerable non-combat units.
2. When you build (or buy) a new unit in a city, it is initially stacked with any units that were already in the city. I'd guess, but have not yet seen, that this can also occur due to receiving a new unit through other means, such as ruins or a city-state gifting a unit to you.

When a unit in the first situation need orders, the game uses the usual message "Unit needs orders" because nothing is wrong. When a unit in this situation needs orders, the game uses the special message "Stacked unit needs orders" to let you know you MUST move a unit.

I got a message for the first time today that said "Move stacked unit". It occurred when I had a great person in my city and another one was generated. Since two non-combat units can't end the turn in the same place, the message was saying that I had to move one of them before I could end my turn.

Since I can't comment yet, I'll clarify WillfulWizard's second bullet in a new answer. When a city-state gifts you a unit, the unit appears within their territory (not in any of your cities).