The American Statistical Association is actively involved in addressing this question. Its Guidelines for Assessment and Instruction in Statistics Education (GAISE) project has recently issued two reports. One of them describes what introductory college-level statistics teaching should cover.
The stated goals are numerous and general. You can read them at http://www.amstat.org/education/gaise/GAISECollege_Goals.pdf. They range from
Students should believe and understand why variability is natural, predictable, and quantifiable
students should know how to interpret statistical results in context.
It is noteworthy that they nowhere mention "binomial," "distribution," or "errors," whereas "inference" is mentioned prominently, as in
Students should understand the basic ideas of statistical inference,
including ... statistical significance [and] ... the concept of confidence interval.
Please be aware that not all introductory statistics courses will follow these guidelines. Courses are taught in various departments for different purposes to a variety of student populations. Some of them, for instance, aim to teach technical methods to students who will later be required to apply them. The best resources for learning the objectives of any particular course of study are (a) its syllabus and (b) the introduction to the textbook, if any. It wouldn't hurt to consult the instructor, either: they should have, ready at hand, a clear and complete answer to this question!