The AfD is something like the Trumpian GOP of Germany. It is described DW AfD video - notable because there doesn't seem much English content about this party. Basically, it's the same as Trumpism - people who are concerned about immigrants, and don't feel heard by the establishment. An important point is that Germany has a much larger welfare state than the US and so Germans are concerned about immigrants taking out from a system into which they put nothing. So, the AfD supporters see two injustices: first, that someone is getting something for nothing, and second, their concerns are being ignored. This core identity of the AfD also comes with a side-order of lingering white-nationalism and neo-nazism, and a helping of anti-democratic sentiment lingering from the East German times.
The lesson for left-wing parties all over the world is clear: you must pay better attention to those people who feel that they've been harmed by idealistic policies. There is nothing wrong with disagreeing with the decision to accept 1 million Syrian refugees. There is nothing inherently racist or even nationalist about this position. But if you don't address that sentiment, the bitterness will quickly turn to hatred and the other qualities will grow.
Maybe its time to get creative. Perhaps instead of having the federal government accept the refugees, individual German families could be given the option of sponsoring a refugee or refugee family, perhaps even with some government assistance. This gives those families who are in support of this policy a way to contribute, and probably yields a healthier integration path for the refugee. Those who don't want to contribute don't have to. It would also give those liberal voters who are supportive in the abstract a chance to do something concretely, and to see the real, day-to-day challenges of integration.