That means the dominant, leading culture. In this case, the one with dominant German values.
This is of course a bad word because it incorrectly implies that Germany should be more like Germany and less like, I dunno, Pakistan or something. That kind of thinking is anti-multikulti and therefore racist not to say Nazi (which will be said soon enough) so when the German interior minister suggests a 10-point plan to help establish these dominant German values – in the hope of actually helping immigrants to integrate – massive waves of righteous moral outrage are virtually guaranteed.*
“Wer sich seiner Leitkultur sicher ist, ist stark.”
* Election time is approaching fast, folks. If this suggestion would have been made by the AfD, by the way, this moral outrage would have been expressed by the very government that just made the suggestion.