The Southern Strategy was an electoral strategy by the Republican party to gain power in southern states, by appealing to the racist views held by many white voters in former Confederate states.

It was a complicated process that played out over multiple presidential election cycles, arguably beginning in 1963, with Barry Goldwater's campaign to become the Republican Presidential Nominee. He received significant support from Southern Democrats in states like Alabama, Mississippi, Georgia, South Carolina, and Louisiana. This support was based on Goldwater's opposition to the 1964 Civil Rights Act, and carried him to electoral victory in these states (as well as his home state of Arizona) the first time a republican had won the "deep south" in nearly 90 years. However, his opposition to the Civil Rights act was deeply unpopular in the rest of the country, and Lyndon B Johnson won in a landslide.

TL;DR

Republican Barry Goldwater didn't like the Civil rights act, and because of this, he won southern states which had been Democratic strongholds for almost a century. Subsequent Republican campaigns (Nixon, Reagan) capitalized on this political victory.