1. Untutored in the perversities of some particular program or system; one who still tries to do things in an intuitive way, rather than the right way (in really good designs these coincide, but most designs aren't ‘really good’ in the appropriate sense). This trait is completely unrelated to general maturity or competence, or even competence at any other specific program. It is a sad commentary on the primitive state of computing that the natural opposite of this term is often claimed to be experienced user but is really more like cynical user.
2. Said of an algorithm that doesn't take advantage of some superior but advanced technique, e.g., the bubble sort. It may imply naivete on the part of the programmer, although there are situations where a naive algorithm is preferred, because it is more important to keep the code comprehensible than to go for maximum performance. “I know the linear search is naive, but in this case the list typically only has half a dozen items.” Compare brute force.