The literal meaning of this phrase in the novel refers to the destruction of documents Winston is engaged with while at work in the Ministry of Truth. His job is to rewrite history, to change the written records of events so that any evidence of facts detrimental to the Party will be wiped out. The old documents are thrown into a receptacle and vaporized (though that term is normally used not for paper but for people in 1984), sucked into a vast futuristic furnace. The receptacle is ironically termed the memory hole because its function is actually to destroy memory, or wipe out the record of the past.
As with other elements of the story, Orwell takes a process that exists in the real world and extends, or exaggerates, it in his depiction of a nightmarish future. This is one of the reasons phrases from 1984 have entered our own lexicon: they refer to things that actually exist and happen. In human affairs, "inconvenient" facts or truths are deliberately consigned to oblivion by political leaders and, less obviously, by people in general. It doesn't occur as systematically (at least not yet) in our world as in Orwell's dystopia, but still, it happens with enough frequency that the phrase "down the memory hole" resonates with us. The phenomenon of forgetting, sometimes deliberately and sometimes not, shows how fragile our hold on reality is, especially when written records are destroyed. If such records no longer exist, having been thrown into a kind of bottomless pit, then the question becomes: what proof is there that the events they attest to actually occurred? Did they occur? How, in the absence of external evidence, can we even know that our own memories are accurate and true?
What is relevant to this issue is the fact that Orwell was writing at a time when computers were still in a primitive state and had not yet become a central element of our culture or an object of the public consciousness. He nevertheless anticipated the process by which computers can be used in a systematic way to erase truths and spread falsehoods. The "speakwrite" Winston uses at work is a computer-like device that rewrites information. While the simple destruction of paper documents, in which they are literally thrown into what's essentially a huge rubbish bin, seems clumsy and antiquated by our standards and by the reality of our time, it's symbolic of the manipulation of facts in the service of power by unscrupulous leaders. The Party's intention is to destroy the concept of objective reality. "Truth" becomes not what people objectively observe and experience (as was actually stated by one such unscrupulous person of our own time: "truth is not truth"), but whatever the Party declares it to be. The memory hole symbolizes this forced "forgetting" on a massive scale.