Phenomenalism is an epistemology or theory of knowledge in which the basic premise is that we can only know that which is validated by our senses. It is similar to Idealism as they both state our only knowledge comes directly from empirical perceptions, we have no innate ideas and can garner nothing about our environment but that which we see, hear, taste, touch and smell. The theory gets its name from the Greek phainomenon meaning that which appears or is seen, used here to refer to our sense experiences.
The most important form of phenomenalism is that of A.J. Ayer, Logical Positivism, in this view a statement can only be true if a sense experience can verify it. For example, I may say that Dem Bones is a genius, but unless I have direct sense data, i.e. I've seen the light and heard the word, my statement cannot be proved true or false. An example used by Ayer is that of a man who says, "I can turn invisible but only when I close my eyes, no one is looking and there are no cameras, etc." This statement cannot be proved true or false and is therefore nonsense; this questioning is called the Verification Principle. The phenomenalist’s view tells them that anything which could possibly be experienced by the senses could exist. In effect, the fact that we could see aliens one day, means that aliens could exist, we could even go so far as to say that every possible facet of the imagination exists in potential. They account for objects we experience everyday as 'permanent possibilities of experience', as opposed to the Idealist view that such objects do not exist.
This verification principle presents one of the main criticisms of Phenomenalism, and Logical Positivism in particular, if anything we cannot verify with our senses is nonsense, then surely any theory about knowledge which cannot be verified by our senses must be nonsense, phenomenalism effectively shoots itself in the foot with its own principles.
A node your homework moment if ever there was one :)