Dual representation is a cognitive skill that emerges in the first few years of life. It consists of recognizing that some objects or pictures can represent other objects.
Infants and toddlers can generally recognize objects in photographs and use objects, including toys, appropriately. However, a year-old baby, seeing a lifelike picture, will attempt to interact with it as if it were an actual object; attempting to put a picture of a shoe on its foot, or a picture of food in its mouth. By the time children are about a year and a half, they start to recognized that photos are representations, and can use them to refer to items (e.g., pointing to a picture of an item they want).
Psychologist Judy DeLoache found a clever way to test if this was really a matter of failing to recognize representation, as opposed to simply a concrete way of playing. She allowed small children to play with a dollhouse set up as a simple furnished room, and then showed the children a toy item (e.g., a small dog), which she hid somewhere in the room (e.g., under the couch). She then showed the children a full-sized room she had set up to look exactly like the dollhouse room, and asked them to find the item, which had been hidden in the same place as in the dollhouse. She found that the three-year-olds could mostly do this (75-90% success rate), but that 30-month-old (2.5 years) children mostly could not (15-20% success rate).
In a variation of the experiment, named 'The Credible Shrinking Room', Deloache had two experimental groups, both comprised of 30-month-old children. One group completed the experiment in the same form as described above, but with the large room presented first and then moving to the miniature room; they achieved similar results (~25% success). Members of the second experimental group were also shown a full sized item in a full sized room, but this time each child was told that the experimenter was going to use a shrinking machine to shrink the room... which they then proceeded to do, showing the child the resultant tiny room. The children in this group, also each 30-months-old (and thus perfectly willing to believe the experimental premise) found the shrunken toy in the shrunken room with ~70% success rate. They apparently had little trouble finding the toy when it was the 'same' toy in the 'same' room (just shrunken); they only had difficulty when dealing with two separate rooms, where a concept of representation -- rather than simply memory -- was required.
It appears that this is a skill that is learned, to some extent, from practice provided by caregivers. For example, children learn to map from a photograph to a real room before they learn to map from the model room to the real room; 30-month-old children did usually manage to find the item if it was shown in a picture (80% success rate). This is presumably because we show young children many many pictures, but few models.
This skill is generally seen as a precursor to symbolic representation as used in reading, math, and abstract thought.