The subconscious is the part of our mind that is not in current awareness. It is the part of our consciousness that is not being focused on and is lying dormant. It is impossible to hold the entirety of our knowledge in direct focus in our minds at the same time so we need to store memories and knowledge. This storage is known as the subconscious, the term being coined by Pierre Janet. The subconscious stores all of your memories, beliefs, previous experiences, the people/places you have seen, and the skills you have acquired. Information in the subconscious cannot be recalled easily, they are buried deep within our minds (or repressed).
The subconscious is not necessarily a psychoanalytic term - the concept was written about before psychoanalytic theory was fully developed. Confusion can often arise between the concepts of the subconscious and the preconscious. The preconscious is a concept in psychoanalytical theory and is different from the subconscious in that the information can be easily brought to mind - it isn't repressed. An example of preconscious thought would be what you ate for dinner last night. Although you were (more than likely) not currently thinking about what you ate you can easily remember what that was. Information in the subconscious cannot be brought to mind as easily.