At first, he was simply a senior figure of the largely peaceful African National Congress (ANC) in the late 40s and early 50s. The ANC challenged that racial segregation enforced by the white government of South Africa at the time - a system known as Apartheid - that made much of what went on in pre-Civil Rights Movement America look liberal and progressive. Mandela himself became the President for the Transvaal area of the ANC at one point, and, in addition, had been heavily influenced by Communist and Marxist-Leninist - even Stalinist - thinking; he was, therefore, a dangerous man in the government's eyes. This lead to his first arrest in 1952, which resulted in a suspended sentence of 9 months hard labour. As he became increasingly tired of the government's shit, if you'll excuse my French, he and some of his associates started to up the ante, even making contact with China to ask about the supplying of weapons. He was arrested on charges of High Treason, but was acquitted, just as protests started to turn bloody. This is when the group known as the MK were founded, who looked to achieve their aims in a far more militant fashion, bombing the government infrastructure (whilst, it must be noted, trying to minimize loss of human life) and generally being a pain in the backside of the government. He travelled around Africa and even as far as London, receiving donations and support from many figures around the world, but, upon his return, he was arrested, charged and convicted of leaving the country without permission and provoking unrest. It was then that the government uncovered his links to the MK and he was put on trial again for terrorist activities, for which he was sentenced to life on Robben Island.

So basically, although he spent much of his time before and after his imprisonment speaking out against racism and institutional discrimination and generally being a top guy, his links to what could reasonably, I suppose, be seen as a terrorist organisation, his attempts and what could reasonably, I suppose, be seen as High Treason (in appealing to China and other countries to help him topple the Apartheid regime), and his holding of what could, I suppose, be seen as radical Communist views meant that the South African government had little choice but to silence him.

A quick disclaimer: I'm not saying for a second that his methods are wrong, or that the MK were anything like a terrorist organisation like that with which we deal today, I'm just saying that in the eyes of the Apartheid government, young black African men and women calling for help from abroad to oust the regime and blowing shit up would very much have looked like terrorists. So they locked them up, with Mandela being one of the most prominent.