The term spoon-feeding is a metaphor, a type of literary comparison that explains one concept in terms of another. It is often used by teachers to talk about student responsibilities.
On a literal level it refers to how parents feed babies. A parent puts a small amount of food on a spoon and lifts it up to the baby's mouth so the baby can eat.
Like most metaphors, what is important is what the image conveys to readers. A baby is small, helpless, and uncoordinated and cannot feed itself. An older child or adult who requires "spoon-feeding" is seen as acting like a baby. An average six year old, for example, should be able to feed himself rather than require spoon-feeding.
When teachers tell students that college classes do not involve "spoon-feeding," they are saying that college students will be treated as able to do work as mature, competent individuals, rather than being treated as babies and having assignments broken down into tiny easy steps. It is both a compliment to a student's maturity and a way of conveying the expectation that students are responsible for keeping up with the syllabus, getting work done on time and asking for help if they need it.