As Vannevar Bush describes the Memex back in 1945: A memex is a device in which an individual stores all his books, records, and communications, and which is mechanized so that it may be consulted with exceeding speed and flexibility. It is an enlarged intimate supplement to his memory."
A core aspect of the Memex is that the selection of information does not work by indexing as it is known from traditional file systems. Instead, Memex supports selection by association, similar to the selection processes that is happening in the human brain. Memex allows the user to create custom associate trails by stitching information from various resources together.
Current hypertext systems build strongly on this idea. This wiki, for example, can be seen as a collaborative Memex.
PDF of As We May Think in which the Memex is described in high detail: