Who said, "Rough seas make good sailors"?
As mentioned above, this quote has many sources and it is more about what it means or implies that is important rather than its origin as a direct quotation. The saying evidently has its beginnings in one or more proverbs and is considered to be something of a cliche (an overused saying). The link between the proverbial sailor who survives a "rough" sea and the average person who must rise to certain life challenges and emerge a better person is apparent. A sailor who survives a rough sea has a perspective he would not have had previously.
Everyone can relate to the sea and to stormy weather and relationships are often compared to rough seas. Therefore, a visual picture is easily created which makes this a good means of relaying a message. A storm is a naturally-occurring event and a sailor uses his knowledge to navigate a storm. Each storm that the sailor successfully steers his ship through makes him a better, more experienced sailor. He will be better equipped for the next one and will have more understanding of his opponent- the sea. If he never has any challenges, the possibility exists that, when he is caught in a storm of seemingly massive proportions, the sailor will be unable to cope and the ship will be destroyed and the sailor (and potentially many others) will die: so too in life. For some, there are many life challenges and when an all-consuming event occurs, they are able to put it in perspective, manage it and move on with life, despite the associated trauma. However, others, when they are faced with an enormous challenge, cannot cope and their relationships fail or their physical or even mental health suffers. In other words, challenges are a necessary part of life; they are character-building and give depth to a situation, allowing a person to see the point of view of another person just as a rough sea is crucial to the development of a good sailor. As Atticus Finch says in To Kill A Mockingbird, challenges allow a person to "climb into another man's skin and walk around in it" (chapter 3).
As Bullgatortail stated, this is what is known as a proverb, a phrase circulated orally across many generations. Versions are common in both English and Swahili, but seem to have developed independently. As such proverbs existed before or independent of writing, we have no record of who first uttered them or how they came into their present form.
The point of the proverb is that you develop skills in face of difficulty. Just as a skier who only skied on beginner slopes or a rock or ice climber who only attempted easy climbs wouldn't hone the skills necessary to handle more difficult situations, so in general, in life we develop skills by stretching ourselves outside of our comfort zone.
In athletics, this might mean pushing yourself to run fast or lift heavy weights. In school, this might mean reading difficult books with unfamiliar words and concepts rather than resorting to summaries (reading Shakespeare's actual plays rather than modernized versions, for example) or choosing difficult classes.
Your exact quote may be taken out of context somewhat, but it has not been credited to any single person. It has been credited as both an old English proverb--"A smooth sea never made a skillful sailor"--as well as an old African (Swahili) proverb--"Smooth seas do not make skillful sailors"--in different forms. Other uncredited variations are "Rough waters make a good sailor;" and "A calm sea cannot produce a good sailor." In any case, the quote is meant to point out that some good can come from even the most difficult situation.