In the context of learning and memory, "retrieval" refers to the act of revisiting information you've already committed to memory.
When we form memories, we encode information and then store that information. Recalling a memory, be it a personal experience or piece of data, like the date when a historical battle was fought, requires we retrieve that encoded information.
This process is what allows us to know things, and to have language and relationships. It's fundamental enough to biological survival that most living things have some kind of information storage and retrieval system—though many such systems are "simpler" in the sense that (as far as we know, at least) there aren't consciousnesses attached to them.
Not all memory—even in humans—is conscious, though.
Declarative (sometimes called "explicit") memory is what we use when we want to remember names and dates and other intentionally stored data.
Non-declarative (sometimes called "implicit") memory is the unconscious storage of things like emotional responses to external stimuli.
So if I want to memorize the date of a historical battle for a test I'll be taking, I'm using my declarative memory, and if I feel embarrassed by a grade I got on a test, my non-declarative memory may capture a snapshot of that embarrassment and could cause me to feel echoes of it when sitting at the same desk or researching the topic of that test in the future.
Retrieval is primarily used to revisit declarative memories, and there's evidence that our retrieval skills can be honed, making our recollection efforts more effective and efficient.
So while endlessly re-reading a passage we wish to learn can eventually allow us to quote that passage, verbatim, it may be more effective to do some re-reading, but then also practice recalling—retrieving—that information from our internal data-storage.
This is considered to be important in part because it helps us not just practice the act of storage for that piece of information but also our retrieval of it. Lacking that latter part of the memory-retrieval axis, we may have vital information stored somewhere in our brains but not be capable of recalling it when necessary.
Repeating this store-retrieve process with many types of data, over time, can be beneficial to our future memorization efforts, as this seems to be a skill that can be honed and exercised.
It's thought that part of the mechanism that allows us to do this is related to how we store things, but part of it is the consequence of our brain changing memories as we retrieve them: each time we summon a piece of data from our memory storage, we adjust it slightly to make it more or less easily retrieved in the future, almost like adding little bits of metadata that make searching for it a more or less ponderous, energy-intensive task the next time we go looking.
Practicing this component of the larger memory process, then, can help us become better memorizers and thinkers, as it brings the information and experiences we have scattered throughout our brains into a more orderly and accessible state.
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