Illusory conjunctions are psychological concepts where participants accidentally combine features of two objects into one object. There are both visual illusory conjunctions and auditory illusory conjunctions. Both types occur due to a lack of attention. Visual attention depends on fixation and amount of time allotted to focus on an object. With a short span of time to interpret an object, blending of different aspects in a visual field, like shapes and colors, can occasionally be skewed which results in visual illusory conjunctions. For example a study designed by Anne Treisman

Anne Treisman

Anne Marie Treisman FRS is a psychologist currently at Princeton University's Department of Psychology. She researches visual attention, object perception, and memory. One of her most influential ideas is the feature integration theory of attention, first published with G. Gelade in 1980...

and Schmidt, required participants to see a visual presentation of black numbers and shapes in different colors. Some shapes were larger than others but all shapes and numbers were evenly spaced and shown for 200 ms. Due to the fact that the shapes and numbers were shown for such a short amount of time, when the participants were asked to recall them they reported answers such as a small green triangle instead of a small green circle. If the space is smaller between objects illusory conjunctions happen more often.
Auditory illusory conjunctions occur in a similar manner, when hearing different sounds one sound is perceived by the individual. An example of auditory illusory conjunctions is the octave illusion. During this study participants heard different tones one high and one low. One was played in the right ear and the other in the left ear. The tones were played at the exact same time for 20 seconds. When asked what the participant heard they reported one tone changing in frequency and location. Limited time caused an auditory illusory conjunction for the participants. Illusory conjunctions occur, both visually and auditory, due to lack of time to focus ones attention to the objects or sounds and perceive them correctly, therefore combining features of different objects.

Attentional requirements

Two objects that are not the focus of attention are also more likely to be combined when they are adjacent to each other. Although it would seem more common for objects to combine when they are not the focus of attention it is also more likely for an illusory conjunction to occur when objects are the focus of attention Illusory conjunctions can occur in long and brief exposure times along with the different levels of
attention paid to the objects involved

Location

Along with the feature integration the location formed from the two objects is a combined result of their locations, but the similarity of the features is what increases the likelihood of an illusory conjunction In order for an illusory conjunction to occur the two objects that are not the focus of attention need to be within the visual field. The closer two objects are the more likely the illusory conjunction to occur

Conjunctions from memory

Illusory conjunctions can occur even when all the stimuli involved is not present. Physical stimuli and images can be combined through a lapse in memory of an
image that is filled by physical stimuli

Non-visual illusory conjunctions

Illusory conjunctions are also not bound to visual stimuli. Auditory stimuli can be combined as
an illusory conjunction through the combination of a pitch and a tone. The greater the number of tones involved in a sequence the greater the likelihood of an illusory
conjunction to occur with a different pitch and a tone

Other theories

There is some debate as to whether or not illusory conjunctions exist as a psychological phenomenon. The main criticism is that research in support of illusory conjunctions is not sufficient enough in the methods used to analyze the data. If this criticism were found to be true it would support the theory that illusory conjunctions are only illusions and nothing more

See also

Anne Treisman: http://psych.princeton.edu/psychology/research/treisman/index.php
Optical Illusions: http://www.acnr.co.uk/pdfs/volume6issue2/v6i2visual.pdf