Underwater basket weaving is a term that used to denote a fictional or useless university course. It is primarily used in a derogatory context to categorize worthless courses that students take to avoid other obligations. Now, however, a handful of universities actually offer this class, making the connotation of this idiom dependent on the context in which it is used. The phrase has been around since the mid-1950s, while the first actual noncredit, informal course on the subject was offered in 1980 by the Reed College in Portland, Oregon.
During the Vietnam war era, a large number of young men took up useless courses to avoid getting drafted. The phrase was used then in the media to highlight the situation, making disparaging remarks about how many young people were opting for underwater basket weaving and other such courses. The phrase can also be used in a number of other contexts, such as mocking the course load taken by typical student athletes. For instance, "Robert, you need to take up advanced chemistry, baseball theory, and underwater basket weaving this year to keep your grades up."
Overall, it is mostly used in a satirical sense to refer to worthless or impractical college courses, a course taken to avoid working too hard, or extremely boring courses. The saying can also showcase how dumb a person can be be; for example, "Shiela is so intelligent that she won the underwater basket weaving competition this year." The phrase can also refer to a very easy kind of university class, perhaps one that isn't required for a person to graduate or sometimes even to answer questions in a humorous fashion. For instance, the question, "Do I need to take a degree in forensic science for this job," could be answered, "As long as you have the right backing, you can have a degree in underwater basket weaving for all that it matters."
These days, the phrase can be legitimately used to refer to actual underwater basket weaving classes. The Reed College offers this course in its seven-day festival known as Paideia. The course teaches students the traditional Inuit way of weaving baskets after soaking the reeds in water. This is done to allow the reeds to become much more flexible, making it easy to weave them into a basket. Mostly though, the phrase is still used in a negative sense, and a few colleges have posted syllabuses for this course on their websites as jokes.