Not realizing what you are doing, or not realizing what is happening around you. As an adjective it almost always sits in front of a noun and describes a person who is part of a situation without knowing it: 'the unknowing victim of a scam', 'an unknowing accomplice', 'unknowing participants in the study'. The key idea is innocence through ignorance — the person really is involved, but they cannot be blamed, because nobody told them.

Because of that, the word is at home in writing about crime, tricks, research, and medicine: someone who carried a bag for a stranger, someone whose photo was used in an advert, someone who passed on a disease. It is a slightly formal, written word. In speech you are much more likely to hear 'She had no idea' or 'without knowing it' — which is exactly what the adverb 'unknowingly' does for you (see that entry).

There is also a noun 'unknowing', meaning the state of not knowing. It is rare and belongs to religious and philosophical writing, most famously in the medieval English book 'The Cloud of Unknowing', where not-knowing is treated as a good and necessary thing on the way to God. If your students meet the noun, it is almost certainly there, or in a writer borrowing that flavour.

One more shade: writers sometimes use 'unknowing' the way they would use 'innocent' or 'unsuspecting', for a mood — 'the unknowing calm of that last summer'. That is a stretch of the word, but a common and beautiful one.