Here is a professor of Middle East history at UCLA explaining some of the history between Saudi Arabia and Qatar.
The Saudi-Qatari quarrel can be traced to back to the conquests that led to the founding of Saudi Arabia in 1932. Only the fact that Qatar was a British protectorate at that time dissuaded the emerging Saudi state from swallowing up the small spit of land on which Qatar is situated.
In the years following Qatari independence in 1971, Qatar and Saudi Arabia quarreled over boundaries. Qatar also struck out on its own in foreign affairs in an effort to wriggle out from under the thumb of its neighbor.
Then, in 1995, Sheikh Tammin bin Hamad, the current ruler of Qatar, took power from his father in a coup d’état. Monarchs in Saudi Arabia and the UAE viewed the coup as a dangerous precedent and plotted a countercoup. The sheikh was to be assassinated. Tammin caught wind of the plot and crushed it, but the bad blood remained.
Fast forward to 2010-11. During the Arab uprisings, Saudi Arabia and Qatar again found themselves at loggerheads. Qatar became a cheerleader for the uprisings through its news empire, al-Jazeera, and through financial and even military assistance to a number of opposition movements. Saudi Arabia became the epicenter of the counter-revolution.