The concept of sense data (singular: sense datum) is very influential and widely used in the philosophy of perception.
Many philosophers have said that the most immediate objects of perception are mental objects -- objects in the mind. So within the mind there are two different items; there is a mental object, which may represent things outside the mind and something that enables awareness such as the process of a perceptual act (see Husserl) or the phenomenon of an inner sense (see Immanuel Kant or Rene Descartes).
For example, according to this widely held view of philosophers, when I see the President on TV the very first thing I perceive is an image of the President in my mind. This image represents the moving picture on the television screen, and that moving picture on the television screen in turn represents the President himself.
These immediate mental objects of perception have been called sense-data, ideas or percepts. So the mental image I am supposed to have of the President is called a visual sense-datum or a visual idea, or a visual percept of the President.
We have mental awareness of those Presidential sense-data -- not with our eyes, of course, because our eyes are in the physical world, and sense-data are in the mind. Those Presidential sense-data are caused by the image of the President on the TV screen. And the sense-data represent the President to us. So generally there are supposed to be mental, internal objects of perception, which represent physical, external objects. "Internal" here just means "inside the mind" (though of course you can guess that that phrase is open to different interpretations). "External" means, correspondingly, "outside the mind" or "in the physical world."
Sensedata are the (alleged) mind-dependent objects that we are directly aware of in perception, and that have exactly the properties they appear to have.
Critics of sensedata have objected to the theory’s commitment to mind-body dualism, its difficulty in locating sensedata in physical space, and its apparent commitment in some cases to sensedata that have indeterminate properties.
Sensedata theorists may wish to respond to this problem by denying (pace Ayer) that the properties of one's sensedata are always transparent to one.
Sensedata are the (alleged) mind-dependent objects that we are directly aware of in perception, and that have exactly the properties they appear to have.
Second, condition (ii): Sensedata theorists believe that the things we are directly aware of in perception are dependent on the mind of the perceiver — they cannot exist unperceived.
The sensedata theory was very popular, perhaps the orthodox view in the philosophy of perception, in the early twentieth century.