Not an expert, but I did a course on Dutch colonialism and as a Dutch historian in general always had more than a limited interest. I'm sure someone here is better suited to answer but I never like to leave people completely without an answer.

South Africa started off as a resupplying point for all ships heading East. Ever since the Dutch VOC (Vereenigde Oost-Indische Compagnie) had started establishing trade there they needed a place to refill their ships on the way. This became Cape Town, at first just a small town with a couple of farmers, but due it's strategic importance and the growth of Dutch trade it kept growing. Farmers (Boeren) eventually started moving land-inwards, populating more and more of the land there in a normal colonizing pattern (much like was done in the Americas).

It must be noted here that at this time probably only around 40% of the settlers were actually Dutch, Germans represented another 40% and French made up the rest. This had to do with both the overpopulation of Germany and a large influx of protestant French into the Netherlands.

Mostly it was a gradual process. Things changed when the French republic conquered the Netherlands and installed his brother Louis-Napoleon as King there after the very short-lived Batavian Republic. Because the Netherlands now served France they were at war with the British who promptly took the strategic and valuable Cape Colony for themselves and then in the Congress of Vienna decided to keep it (the newly installed Dutch King was compensated as he gained Belgium and Luxembourg, as well as the title King). Basically a lot of Boers kept migrating further inland and founded self-governing states like Transvaal and the Orange Free State while the coastal provinces Anglicised better (although not totally as the prevalence of Afrikaans as a language still demonstrates). It wasn't until the discovery of the valuable Diamond mines deeper inland that the British really grew an interest in subdueing the Boers, which led to a series of bloody wars that humiliated the English, but eventually saw direct Imperial control established over all of Southern Africa.

Adding to /u/GustavGustavson , the VOC trade with Oost-Indische was very important, and to reach Oost-Indische one had to sail through the tip of South Africa and then eastwards to South-East Asia.

For the first leg, one could rely on the steady currents of North and South Atlantic. For the second leg, the trade winds of the Indian Ocean area seasonal. Here's a nice discussion on Encyclopedia Britannica on the subject.

As a result, beyond the need to replenish supplies it is important to have the Cape Colony station as the ships may have a wait quite a while for favorable winds.

And if I could add a question, I have heard in the past that the first Dutch colony on the cape was an attempted move to establish a colony in South America but due to winds or something of the sort they landed in the cape instead and decided to settle, where do these stories originate and did they have any basis in reality?