What is the figurative meaning of "pivot towards"?

You have to understand a bit about US electoral politics. To oversimplify things a bit, there are only two political parties that can nominate a candidate likely to win the general (national) election -- the Republicans (call them the party of the right) and the Democrats (call them the party of the left). Each party selects its nominee in a series of electoral contests that take place in the individual states before the general election. For the most part, the voters in the Republican nominating contests are members of the Republican Party, and likewise for the Democrats. Thus to get the nomination of their parties, candidates must appeal to their own party voters. And the more hotly contested the nominating process becomes, the more the candidates strive to please their own party members. Thus, in a hotly-contested Republican race, Republican candidates voice a conservative message to their supporters. In a hotly-contested Democratic race, Democrats deliver a liberal message. But in the general election in which everyone eligible may vote regardless of party affiliation, a winning candidate has to move to the center.

Once a candidate is assured of winning the nomination, that candidate usually "pivots" (as you say, turns) toward that center position necessary to win the general election. The news writer felt that Clinton's victory in the South Carolina contest -- she beat her opponent, Sanders by 3:1 -- signaled that she had the nomination wrapped up. And thus she could turn toward the center.

Clinton's loss in the Michigan primary means that she can't turn just yet.

now focus on

Clinton's dominating victory in South Carolina’s Democratic primary allows her to now focus on a general-election campaign message.

I wouldn't call it figurative; abstract, perhaps.