Your original question simply asked about the significance of the province/dominion. I have added on to it because of your tags and because you have been asking questions about the British Empire, the Boer War, and the Scramble for Africa.
The major significance of the creation of the Union of South Africa was that it put an end to the tensions that led to the Boer Wars. These were tensions that had arisen because of the presence of mainly Dutch "Boers" who had left the British Cape Colony and created their own free republics. By creating a province that included the former Boer republics, the British united them with the British colonies and gave both ethnic groups equal status within the union.
It is important to note that this was a very accommodating action by the British. It showed that they were willing to put the Boer War behind them (it ended only eight years before the creation of the Union of South Africa) and to essentially give the Boers the independence that they had been fighting for in the Boer Wars.
The significance of the Union, then, is that it ended the Boer War era in a way that was in effect a compromise between the British desire to control the region and the Boers' desire for independence.