Depth of Knowledge refers to how thoroughly you know and understand what
you have been studying.
Recognizing information seen before but not memorized. Information is familiar and you can relate parts when both are presented separately. This is what is mostly tested by multiple-choice tests. Never mistake scoring well on most multiple-choice texts as real learning.
Remembering information, memorizing lists & facts - building up your internal data bank. Working from memory you can present key facts and relationships that you have studied. This is a necessary foundation for deeper learning. If you cannot remember details, then you cannot reason from them. Too often this step is skimped in modern schooling; rote memorization is often necessary for real learning to take place. The most important thing to remember here is that you must PAY ATTENTION to what you are trying to remember. Repeated exposure is necessary for memorization - but you also have to pay attention to the material. The better you pay attention, the less it will need to be repeated for real learning to take place. Having a theoretical framework for the material to fit will also help since we remember mostly by association, this helps recall that. Recall is best tested by fill-in-the-blank type tests and short essay-type questions.
Because memorization is so time and effort intensive, don't waste your time memorizing things that are not important. First, you must remember the basics - arithmetic, spelling, vocabulary, and grammar. Next, you must remember things that you may need without time or references available, when you need them, first aid and various other emergency skills. While learning, you need to memorize things that further learning will depend on, the basic facts and relationships in whatever field you are studying. Finally, when actually working in a field, you need to remember frequently used information that it would waste considerable time looking up repeatedly. These are also important to keep in mind, because to keep things memorized, you need to refresh the memory periodically. The first and last categories you will actually keep refreshed, if you are conscientious in their use by using them. The hardest to keep up on is the second category, emergency skills.
In the third level of knowledge, you understand the material and are able to explain things in your own words. You can draw new relationships between facts. You need to be able to remember details to explain things in your own words - for a long time I deluded myself that I could understand the material because I could follow along with the explanation easily enough as I read it. But you do not truly understand something until you can explain it in your own words from memory.
Finally, you can use information in papers and discussions to articulate and defend what you know. You know the subject well enough to do independent, original research. Here you are learning in your subject primarily by working in the field rather than from others.